# Korrelationstage 2021

## korrel21 Poster Prizes

poster prize of the 1st poster session - Alla Bezvershenko, Universität zu Köln
poster prize of the 2nd poster session - Alessio Lerose, University of Geneva
poster prize of the 3rd poster session - Tiago Mendes Santos, MPIPKS Dresden
poster prize of the 4th poster session - Anne-Maria Visuri, University of Bonn

### Floquet vortex states induced by light carrying the orbital angular momentum

We propose a scheme to create an electronic Floquet vortex state by irradiating the circularly-polarized laser light carrying non-zero orbital angular momentum on the two-dimensional semiconductor. We analytically and numerically study the properties of the Floquet vortex states, using methods analogous to the techniques used for the analysis of superconducting vortex states, and we show that such Floquet vortex states have a wide tunability range. To illustrate the impact of such tunability, we propose how such states could be used for quantum information processing.

### Interaction of a Neel-type skyrmion and a superconducting vortex

Andriyakhina, Elizaveta

Superconductor-ferromagnet heterostructures hosting vortices and skyrmions are new area of an interplay between superconductivity and magnetism. We study an interaction of a Neel-type skyrmion and a Pearl vortex in thin heterostructures due to stray fields. Surprisingly, we find that it can be energetically favorable for the Pearl vortex to be situated at some nonzero distance from the center of the Neel-type skyrmion. The presence of a vortex-antivortex pair is found to result in increase of the skyrmion radius. Our theory predicts that a spontaneous generation of a vortex-anti-vortex pair is possible under some conditions in the presence of a Neel-type skyrmion.

### Exotic phases of cluster-forming systems

I will present my recent results on bosonic systems featuring extended-range interactions, of interest for experiments with cold Rydberg-dressed atoms. In my previous work, I proved these Hamiltonians to host a wide variety of interesting physical phenomena, including (super)solid phases of clusters of particles, as well as out-of-equilibrium glass and superglass states (the latter displaying the coexistence of glassy physics and superfluidity). In this talk, I will discuss my demonstration, in the ground-state regime of this class of models, of a novel type of phase transition between two supersolid states characterized by different crystalline and superfluid exchange structures. I will then discuss my results on the out-of-equilibrium counterparts of the states mentioned above, which I prove to be glasses and (super)solids (the latter featuring crystalline structures in general remarkably different from their ground-state counterparts) in an energy range which would allow their observation in experimental realizations.

Ardila, Luis

### Broken-Symmetry Ground States of Quantum Magnetism on the Pyrochlore Lattice

Astrakhantsev, Nikita

The spin-1/2 Heisenberg model on the pyrochlore lattice is an iconic frustrated three-dimensional spin system with a rich phase diagram. Besides hosting several ordered phases, the case with only nearest-neighbor antiferromagnetic interactions is debated for potentially realizing a spin-liquid ground state. Here, we contest this hypothesis with an extensive numerical investigation using both exact diagonalization and several complementary variational techniques. Specifically, we employ a Pfaffian-type many-variable Monte Carlo ansatz and convolutional neural network quantum states for calculations with up to $3\times 4^3$ and $3 \times 3^3$ spins, respectively. We demonstrate that these techniques yield consistent results, allowing for reliable extrapolations to the thermodynamic limit. Our main results are (1) a determination of the phase transition between the putative spin liquid phase and the neighboring magnetically ordered phase and (2) a careful characterization of the ground state in terms of symmetry breaking tendencies. We find clear indications for spontaneously broken inversion and rotational symmetry, calling the quantum spin-liquid scenario into question. Our work showcases how many-variable variational techniques can be used to make progress in answering challenging questions about three-dimensional frustrated quantum magnets.

### Effect of disorder on topological charge pumping in the Rice-Mele model

Bertok, Eric

Recent experiments with ultracold quantum gases have successfully realized integer-quantized topological charge pumping in optical lattices. Motivated by this progress, we study the effects of static disorder on topological Thouless charge pumping. We focus on the half-filled Rice-Mele model of free spinless fermions and consider random diagonal disorder. In the instantaneous basis, we compute the polarization, the entanglement spectrum, and the local Chern marker. As a first main result, we conclude that the space-integrated local Chern marker is best suited for a quantitative determination of topological transitions in a disordered system. In the time-dependent simulations, we use the time-integrated current to obtain the pumped charge in slowly periodically driven systems. As a second main result, we observe and characterize a disorder-driven breakdown of the quantized charge pump. There is an excellent agreement between the static and the time-dependent ways of computing the pumped charge. The topological transition occurs well in the regime where all states are localized on the given system sizes and is therefore not tied to a delocalization-localization transition of Hamiltonian eigenstates. For individual disorder realizations, the breakdown of the quantized pumping occurs for parameters where the spectral bulk gap inherited from the band gap of the clean system closes, leading to a globally gapless spectrum. As a third main result and with respect to the analysis of finite-size systems, we show that the disorder average of the bulk gap severely overestimates the stability of quantized pumping. A much better estimate is the typical value of the distribution of energy gaps, also called mode of the distribution.

### Dicke transition in open many-body systems determined by fluctuation effects

Bezvershenko, Alla

In recent years, one important experimental achievement was the strong coupling of quantum matter and quantum light. Realizations reach from ultracold atomic gases in high-finesse optical resonators to electronic systems coupled to THz cavities. The dissipative nature of the quantum light field and the global coupling to the quantum matter leads to many exciting phenomena such as the occurrence of dissipative quantum phase transition to self-organized exotic phases. Here we develop a new approach which combines a mean-field approach with a perturbative treatment of fluctuations beyond mean-field, which becomes exact in the thermodynamic limit. We argue that these fluctuations are crucial in order to determine the mixed state (finite temperature) character of the transition and to unravel universal properties of the self-organized states. We validate our results by comparing to time-dependent matrix-product-state calculations.

### Spin and charge order in doped spin-orbit coupled Mott insulators

Biderang, Mehdi

We study a two-dimensional single band Hubbard Hamiltonian with antisymmetric spin-orbit coupling. We argue that this is the minimal model to understand the electronic properties of locally non-centrosymmetric transition-metal (TM) oxides such as Sr$_2$IrO$_4$. Based on exact diagonalizations of small clusters and the random phase approximation, we investigate the correlation effects on charge and magnetic order as a function of doping and of the TM-oxygen-TM bond angle $\theta$. For small doping and $\theta\lesssim$ 15° we find dominant commensurate in-plane antiferromagnetic fluctuations while ferromagnetic fluctuations dominate for $\theta\gtrsim$ 25°. Moderately strong nearest-neighbor Hubbard interactions can also stabilize a charge density wave order. Furthermore, we compare the dispersion of magnetic excitations for the hole-doped case to resonant inelastic X-ray scattering data and find good qualitative agreement.

### Spectroscopy of doped quantum magnets -- new directions

Bohrdt, Annabelle

Single-particle spectral functions, which are usually measured using photoemission experiments in electron systems, contain direct information about fractionalization and the quasiparticle excitation spectrum. In this talk, I will present recent developments that enable angle-resolved photo-emission spectroscopy (ARPES) of the one- and two-dimensional Fermi-Hubbard model using ultra cold atoms in optical lattices. I will discuss numerical results for the one-dimensional t-J model, where a sharp asymmetry in the distribution of spectral weight appears, that can be explained by a slave-fermion mean-field theory of the spin excitations (spinons). By employing a time-dependent ARPES protocol, akin to pump probe experiments in solids, we directly reveal interaction effects between the spinons. While in one dimension the spin (spinon) and charge (chargon) excitations are deconfined, several theories suggest that in two dimensions, dopants can be understood as bound states of these partons. Recent progress in the microscopic description of mobile dopants allows us to conjecture a one-to-one relation of the one-dopant spectral function and the properties of the constituting spinons in the undoped parent antiferromagnet (AFM). Using time-dependent matrix product state calculations of the spectral function of a single hole doped into a two-dimensional Heisenberg AFM, we thoroughly test this hypothesis and obtain excellent agreement with our semi-analytical predictions. We directly probe the microscopic nature of the spinon-chargon bound states through a new extension of ARPES, which uncovers long-lived rotational resonances. Similar to Regge trajectories in high-energy physics, which reflect the quark structure of mesons, we establish a linear dependence of the rotational energy on the super-exchange coupling. Our findings suggest that the rich physics of lightly doped cuprates may originate from an emergent parton structure.

### Skyrmion and Tetarton Lattices in Twisted Bilayer Graphene

Bömerich, Thomas

Recent experiments on twisted bilayer graphene show an anomalous quantum Hall (AQH) effect at filling of three electrons per moiré unit cell. The AQH effect arises in an insulating state with both valley and ferromagnetic order. We argue that weak doping of such a system leads to the formation of a novel topological spin texture, a "double-tetarton lattice". The building block of this lattice, the "double-tetarton", is a spin configuration which covers 1/4 of the unit sphere twice. In contrast to skyrmion lattices, the net magnetization of this magnetic texture vanishes. Only at large magnetic fields are more conventional skyrmion lattices recovered. But even for large fields the addition of a single charge to the ferromagnetic AQH state flips hundreds of spins. Our analysis is based on the investigation of an effective nonlinear sigma model which includes the effects of long-ranged Coulomb interactions.

### Dynamical functional renormalization group computation of order parameters and critical temperatures in the two-dimensional Hubbard model

Bonetti, Pietro Maria

We analyze the interplay of antiferromagnetism and pairing in the two-dimensional Hubbard model with a moderate repulsive interaction. Coupled charge, magnetic, and pairing fluctuations above the energy scale of spontaneous symmetry breaking are treated by a functional renormalization group flow, while the formation of gaps and order below that scale is treated in mean-field theory. The full frequency dependences of the interaction vertices and gap functions are taken into account. We compute the magnetic and pairing gap functions as a function of doping $p$ and compare with results from a static approximation. In spite of the strong frequency dependences of the effective interactions and of the pairing gap, important physical results from previous static functional renormalization group calculations are confirmed. In particular, there is a sizable doping regime with robust pairing coexisting with Néel or incommensurate antiferromagnetism. The critical temperature for magnetic order is interpreted as the pseudogap crossover temperature. Computing the Kosterlitz-Thouless temperature from the superfluid phase stiffness, we obtain a superconducting dome in the $(p,T)$ phase diagram centered around $15\%$ hole doping.

### Bosonic continuum theory of one-dimensional lattice anyons

Bonkhoff, Martin

Anyons with arbitrary exchange phases exist on 1D lattices in ultracold gases. Yet, known continuum theories in 1D do not match. We derive the continuum limit of 1D lattice anyons via interacting bosons. The theory maintains the exchange phase periodicity fully analogous to 2D anyons. This provides a mapping between experiments, lattice anyons, and continuum theories, including Kundu anyons with a natural regularization as a special case. We numerically estimate the Luttinger parameter as a function of the exchange angle to characterize long-range signatures of the theory and predict different velocities for left- and right-moving collective excitations.

### Quantum phases of two-dimensional Z2 gauge theory coupled to single-component fermion matter

Borla, Umberto

We investigate the rich quantum phase diagram of Wegner's theory of discrete Ising gauge fields interacting with U(1) symmetric single-component fermion matter hopping on a two-dimensional square lattice. In particular limits the model reduces to (i) pure $Z_2$ even and odd gauge theories, (ii) free fermions in a static background of deconfined $Z_2$ gauge fields, (iii) the kinetic Rokhsar-Kivelson quantum dimer model at a generic dimer filling. We develop a local transformation that maps the lattice gauge theory onto a model of $Z_2$ gauge-invariant spin 1/2 degrees of freedom. Using the mapping, we perform numerical density matrix renormalization group calculations that corroborate our understanding of the limits identified above. Moreover, in the absence of the magnetic plaquette term, we reveal signatures of topologically ordered Dirac semimetal and staggered Mott insulator phases at half-filling. At strong coupling, the lattice gauge theory displays fracton phenomenology with isolated fermions being completely frozen and dimers exhibiting restricted mobility. In that limit, we predict that in the ground state dimers form compact clusters, whose hopping is suppressed exponentially in their size. We determine the band structure of the smallest clusters numerically using exact diagonalization.

### Realizing a symmetry-protected topological phase in the antiferromagnetic spin-1/2 Hubbard ladder

Bourgund, Dominik

The spin-1 Haldane chain is the paradigmatic example of symmetry protected topological (SPT) phases, which are characterized by non-local order parameters and edge states. Here we report on the experimental realization of such a phase using ultracold fermions in optical lattices. Site-resolved potential shaping allows us to create a tailored spin-1/2 ladder geometry needed to explore the topologically nontrivial Haldane phase. Harnessing the full spin and density resolution of our Fermi-gas microscope, we detect a finite non-local string correlator in the bulk and localized spin-1/2 states at the edges. We confirm the robustness of the state by tuning the ratio of the leg to rung coupling of the ladder. We finally go beyond the spin model and explore the effect of charge fluctuations on the SPT phase in the general Hubbard regime.

### Electronuclear Quantum Criticality

Brando, Manuel

We present here a rare example of electronuclear quantum criticality in a metal. The compound YbCu4.6Au0.4 is located at an unconventional quantum critical point (QCP). In this material the relevant Kondo and RKKY exchange interactions are very low, of the order of 1K. Furthermore, there is a strong competition between antiferromagnetic and ferromagnetic correlations, possibly due to geometrical frustration within the fcc Yb sublattice. This causes strong spin fluctuations which prevent the system to order magnetically. Because of the very low Kondo temperature the Yb3+ 4f-electrons couple weakly with the conduction electrons allowing the coupling to the nuclear moments of the 171Yb and 173Yb isotopes to become important. Thus, the quantum critical fluctuations observed at the QCP derive not from purely electronic states but from entangled electronuclear states. This is evidenced in the anomalous temperature and field dependence of the specific heat at low temperatures.

### Finite-momentum energy dynamics in a Kitaev magnet

Brenig, Wolfram

We study the energy-density dynamics at finite momentum of the two-dimensional Kitaev spin-model on the honeycomb lattice. Due to fractionalization of magnetic moments, the energy relaxation occurs through mobile Majorana matter, coupled to a static $\mathbb{Z}_{2}$ gauge field. At finite temperatures, the $\mathbb{Z}_{2}$ flux excitations act as an emergent disorder, which strongly affects the energy dynamics. We show that sufficiently far above the flux proliferation temperature, but not yet in the classical regime, gauge disorder modifies the coherent low-temperature energy-density dynamics into a form which is almost diffusive, with hydrodynamic momentum scaling of a diffusion-kernel, which however remains retarded, primarily due to the presence of two distinct relaxation channels of particle-hole and particle-particle nature. Relations to thermal conductivity are clarified. Our analysis is based on complementary calculations in the low-temperature homogeneous gauge and a mean-field treatment of thermal gauge fluctuations, valid at intermediate and high temperatures.

### Chiral transitions in chains of Rydberg atoms

Chepiga, Natalia

Investigation of the nature of commensurate-incommensurate transition out of period-p phase has a long history that goes back to the study of absorbed monolayers on surfaces. The problem has been revived by recent experiments on Rydberg atoms in 1D trap with the phase diagram dominated by lobes of integer periodicities p=2,3,4,5… Recent development of constrained DMRG algorithm that takes a full advantage of Rydberg blockade brings the study of chiral melting to a completely new level of accuracy. In my talk I will shown that transitions out of period-3 and period-4 phases change their nature along the critical lines: conformal points in the three-state Potts and Ashkin-Teller universality classes are surrounded by direct chiral transitions followed by the opening of floating phases. Numerical detection of chiral transitions brings the first consistent explanation of dynamical critical exponent z>1 deduced from recent Harvard experiments. I will explain that an appearance of the chiral transition is a generic feature of phases where the number of particles is not conserved because the Luttinger liquid parameter of the floating phase changes along the Pokrovsky-Talapov transition and can thus reach the value at which the floating phase becomes unstable.

### Lieb-Robinson bounds and out-of-time order correlators in a long-range spin chain

Colmenárez Gómez, Luis Andres

Lieb-Robinson bounds quantify the maximal speed of information spreading in nonrelativistic quantum systems. We discuss the relation of Lieb-Robinson bounds to out-of-time order correlators, which correspond to different norms of commutators C(r,t) = [Ai(t), Bi+r] of local operators. Using an exact Krylov space-time evolution technique, we calculate these two different norms of such commutators for the spin-1/2 Heisenberg chain with interactions decaying as a power law 1/rα with distance r. Our numerical analysis shows that both norms (operator norm and normalized Frobenius norm) exhibit the same asymptotic behavior, namely, a linear growth in time at short times and a power-law decay in space at long distance, leading asymptotically to power-law light cones for α < 1 and to linear light cones for α > 1. The asymptotic form of the tails of C(r,t) ∝ t/rα is described by short-time perturbation theory, which is valid at short times and long distances.

### Effect of nonmagnetic dilution on magnetic properties of frustrated oxyborates

Contreras Medrano, Cynthia

Magnetic oxyborates of the 3d transition metals are good examples of strongly correlated systems in which magnetic frustration and structural disorder have often been observed [1,2]. Low-dimensional substructures are characteristic of these compounds, and they are present in the form of ladders in ludwigites, ribbons in warwickites, and planes in hulsites. These compounds have shown complex and intriguing physical properties that depend on their elementary composition. Nonmagnetic ions are usually used to reduce magnetic interactions in an effort to understand these complex magnetic compounds. However, heterometallic ludwigites with different nonmagnetic ions displayed distinct properties as metamagnetic transition, partial magnetic order, spin-glass, fluctuations, making these compounds fundamentally more interesting. A summary of these effects is listed in this presentation.

### Kondo Breakdown in a Spin-1/2 Chain of Adatoms on a Dirac Semimetal

Danu, Bimla

We consider a spin-1/2 Heisenberg chain coupled via a Kondo interaction to two-dimensional Dirac fermions. The Kondo interaction is irrelevant at the decoupled fixed point, leading to the existence of a Kondo-breakdown phase and a Kondo-breakdown critical point separating such a phase from a heavy Fermi liquid. We reach this conclusion on the basis of a renormalization group analysis, large-N calculations as well as extensive auxiliary-field quantum Monte Carlo simulations. We extract quantities such as the zero-bias tunneling conductance which will be relevant to future experiments involving adatoms on semimetals such as graphene.

### Resonant inelastic x-ray scattering study of vector chiral ordered kagome antiferromagnet

Datta, Trinanjan

We study the resonant inelastic x-ray scattering (RIXS) features of vector chiral ordered kagome antiferromagnets. Utilizing a group theoretical formalism that respects lattice site symmetry, we calculated the L-edge magnon contribution for the vesignieite compound BaCu$_3$V$_2$O$_8$(OH)$_2$. We show that polarization dependence of the L-edge RIXS spectrum can be used to track magnon branches. We predict a non-zero L-edge signal in the non-cross $\pi-\pi$ polarization channel. At the K-edge, we derived the two-site effective RIXS and Raman scattering operator for two-magnon excitation in vesignieite using the Shastry–Shraiman formalism. Our derivation considers spin-orbit coupling effects in virtual hopping processes. We find vector chiral correlation (four-spin) contribution that is proportional to the RIXS spectrum. Our scattering operator formalism can be applied to a host of non-collinear non-coplanar magnetic materials at both the L and K-edge. We demonstrate that vector chiral correlations can be accessed by RIXS experiments.

### Construction of low-energy symmetric Hamiltonians and Hubbard parameters for twisted multilayer systems using ab-initio input

A computationally efficient workflow for obtaining the low-energy symmetric tight-binding Hamiltonians for twisted multilayer systems is presented in this work. We apply this scheme to the twisted bilayer graphene at the first magic angle. As the initial step, the full-energy tight-banding Hamiltonian is generated by the Slater-Koster model with parameters fitted to ab-initio data at larger angles. Then, the low-energy symmetric four-band and twelve-band Hamiltonians are constructed using the maximum-localization procedure subjected to the crystal and the developed time-reversal symmetry constraint. Finally, we compute extended Hubbard parameters for both models within the constrained random phase approximation (cRPA) for screening, which again respect the symmetries. The relevant data and results of this work are freely available via an online repository. The workflow is straightforwardly transferable to other twisted multi-layer materials.

### Multifractality meets entanglement: relation for non-ergodic extended states

De Tomasi, Giuseppe

It is now well established that entanglement plays a central role on the thermalization process of quantum many-body systems. On the other hand, ergodicity is deeply connected to the notion of chaos, which implies also an equipartition of the wave-function over the available many-body Fock states, which is usually quantified by multi-fractal analysis. In this talk, I will discuss a link between ergodic properties extracted from entanglement entropy and the ones from multi-fractal analysis [1]. I will show a generalization of the work of Don. N. Page [2] for the entanglement entropy, to the case of non-ergodic but extended (NEE) states. By implementing the NEE states with a new and simple class of random states, which live in a fractal of the Fock space, I will compute, both analytically and numerically, its von Neumann/Renyi entropy. Remarkably, I will show that the entanglement entropies can still present a fully ergodic behavior, even though the wave-function lives in a vanishing ratio of the full Hilbert space in the thermodynamic limit. In the final part of the talk, I will apply the aforementioned results to analyze the breakdown of thermalization in kinematically constrained models having Fock/Hilbert space fragmentation [3]. References: [1] Phys. Rev. Lett. 124, 200602 (2020) [2] Phys. Rev. Lett. 71, 1291 (1993) [3] Phys. Rev. B 100, 214313 (2019)

### Extraction of many-body Chern number from a single wave function

Dehghani, Hossein

The quantized Hall conductivity of integer and fractional quantum Hall (IQH and FQH) states is directly related to a topological invariant, the many-body Chern number. The conventional calculation of this invariant in interacting systems requires a family of many-body wave functions parameterized by twist angles in order to calculate the Berry curvature. In this paper, we demonstrate how to extract the Chern number given a single many-body wave function, without knowledge of the Hamiltonian. For FQH states, our method requires one additional integer invariant as input: the number of 2

### Non-Abelian Bloch oscillations in higher-order topological insulators

Di Liberto, Marco

Bloch oscillations (BOs) are a fundamental phenomenon by which a wave packet undergoes a periodic motion in a lattice when subjected to a force. Observed in a wide range of synthetic systems, BOs are intrinsically related to geometric and topological properties of the underlying band structure. This has established BOs as a prominent tool for the detection of Berry-phase effects, including those described by non-Abelian gauge fields. In this work, we unveil a unique topological effect that manifests in the BOs of higher-order topological insulators through the interplay of non-Abelian Berry curvature and quantized Wilson loops. It is characterized by an oscillating Hall drift synchronized with a topologically-protected inter-band beating and a multiplied Bloch period. We elucidate that the origin of this synchronization mechanism relies on the periodic quantum dynamics of Wannier centers. Our work paves the way to the experimental detection of non-Abelian topological properties through the measurement of Berry phases and center-of-mass displacements.

### The quasi-1D Lieb-Liniger gas in a trap with time-periodically modulated interactions

Eggert, Sebastian

We consider the exactly solvable Lieb-Liniger model of quasi-1D interacting bosonic atoms with time-periodically modulated interactions. Using recent advances for a Floquet-Bogoliubov rotation, we are able to obtain the Floquet eigenstates exactly in the long-wavelength limit, i.e. for wave-numbers below a cut-off $q_c$. We observe a dramatic change of behavior in the appearance of resonant density waves as the frequency $\omega$ is lowered through the corresponding energy scale, which corresponds to around $2 \pi \times$kHz in typical experimental systems. The wavelength of the resonant waves is proportional to the square-root of the average density, becoming shorter near the edges of the confining trap, while in the center the maximum is in the $\mu$m range.

### Breakdown of the Doniach picture: From single impurity physics to correlated lattice models

Eickhoff, Fabian

In order to understand the competition between the RKKY and Kondo driven screening of local moments and to shed some new light on Nozières exhaustion argument, we present a low energy mapping of multi-impurity Anderson models with $N_f$ correlated sites to a cluster model coupled to $N_c$ independent conduction bands. This mapping becomes exact in the wide band limit, is applicable for arbitrary strengths of interaction and doesn't rely on any kind of symmetry. The rigorous mathematical criterion for determining $N_c$ replaces the phenomenological exhaustion argument and reveals that there are always insufficient Kondo screening channels available in the periodic Kondo or Anderson model: The singlet ground state formation must be driven by the inter-cluster spin correlations. As an application of the mapping we study the effect of local vacancies in multi impurity models using the NRG. These vacancies in graphene or in Heavy Fermions induce decoupled bound single particle states that lead to the formation of local moments. We address the puzzling question how these local moments can be screened and what determines the additionally emerging low temperature scale.

### Universal aspects of constrained quantum systems out of equilibrium

Feldmeier, Johannes

As advances in the technology of quantum simulation provide increasing control over complex many-body systems, the study of their out-of-equilibrium properties is gaining attention. While a full theoretical description of the unitary evolution is in general challenging to obtain, we can rely on a notion of universality to describe the quantum thermalization process: after a local equilibration time, emergent hydrodynamics describes the diffusive transport of conserved quantities through the system, accompanied by a linear-in-time growth of entanglement. Here we discuss how such universal aspects of the late time dynamics in quantum many-body systems can be drastically altered in the presence of constraints. In particular, we first show how systems that are constrained to conserve the dipole moment of an associated global charge generally display anomalously slow subdiffusive transport, consistent with recent cold atom experiments. We investigate these systems numerically using classically simulable circuits and construct an analytical hydrodynamic theory that yields the correct scaling of local correlations at late times. We then go on to demonstrate how the presence of constraints in such fractonic quantum matter - characterized by excitations with restricted mobility - can further lead to an anomalously slow growth of entanglement.

### Variational wave functions for spin-phonon models

Ferrari, Francesco

The existence and stability of spin-liquid phases represent central topics in the field of frustrated magnetism. In the last few years, a large theoretical effort has been devoted to proposing and studying frustrated spin models which could host spin-liquid ground states. Although several examples of well-established spin-liquid phases are now available, the question of the stability of these states to the coupling between spins and lattice distortions (i.e. phonons) has been scarcely investigated. As suggested by the well-known one-dimensional case, the effect of lattice deformations could cause a Peierls instability of spin-liquid phases towards the formation of valence-bond order. We present a variational framework for the study of spin-phonon models in which lattice distortions affect the exchange interaction between the spins. Our method, based on Jastrow-Slater wave functions and Monte Carlo sampling, provides a full quantum treatment of both spin and phonon degrees of freedom. We first assess the accuracy of our variational scheme by comparing our results for the spin-Peierls chain with other numerical methods [1]. Then, we discuss the effects of the spin-phonon coupling on the spin liquid phase of the square lattice J1-J2 model. [1] F. Ferrari, R. Valenti, F. Becca, Phys. Rev. B 102, 125149 (2020).

### Quantized Electrochemical Transport in Weyl Semimetals

Flores Calderón, Rafael Álvaro

We show that under the effect of an external electric field and a gradient of chemical potential, a topological electric current can be induced in Weyl semimetals without inversion and mirror symmetries. We derive analytic expressions for the nonlinear conductivity tensor and show that it is nearly quantized for small tilting when the Fermi levels are close to the Weyl nodes. When the Van Hove point is much larger than the largest Fermi level, the band structure is described by two linearly dispersing Weyl fermions with opposite chiralities. In this case, the electrochemical response is fully quantized in terms of fundamental constants and the scattering time, and it can be used to measure directly the topological charge of Weyl points. We show that the electrochemical chiral current may be derived from an electromagnetic action similar to axion electrodynamics, where the position-dependent chiral Fermi level plays the role of the axion field. This posits our results as a direct consequence of the chiral anomaly.

### Semi-classical Dynamics of Magnetic Field-Induced Phases in Kitaev Magnets

Franke, Oliver

The Kitaev honeycomb model with a finite $\Gamma$ interaction shows a multitude of magnetic field induced phases between the low field zigzag and the high field polarised regime. These intermediate phases often posses large unit cells at finite magnetic fields and their relation with the experimentally measured phase diagram of RuCl$_3$ is unclear. Here, we study these competing phases with advanced stochastic LLG simulations and present their static and dynamic structure factors. There are sharp low-frequency spin-waves which broaden quickly at elevated frequencies. While the different intermediate orders with large unit cells are clearly distinguishable in their structure factors for low-temperatures their broad response for experimentally relevant temperatures looks remarkably similar.

### $^{93}$Nb NMR study of 2D superconductivity in van der Waals heterostructures

Frassineti, Jonathan

The purpose of this work is the study of physical symmetries and charge-related properties in a bulk superlattice, consisting of the transition metal dichalcogenide (TMD) superconductor 2H-niobium disulfide (2H-NbS$_{2}$) and a commensurate block layer. This study will be conducted by performing Nuclear Magnetic Resonance (NMR) experiments on $^{93}$Nb nuclei, which are suitable to this technique due to their high sensitivity to NMR and high abundancy. Considerable efforts have been carried out to reach 2D superconductivity in transition metal dichalcogenides (TMDs). These materials present intrinsically strong spin-orbit coupling and inversion symmetry breaking, which may yield to exotic forms of superconductivity in the clean limit, when the Pippard coherence length, $\xi_{0}$, is smaller than the electronic mean-free path, $l$, i.e $\frac{\xi_{0}}{l} \ll 1$. High-quality H-NbS$_{2}$ monolayers with electronic mobilities more than three orders of magnitude larger than in bulk 2H-NbS$_{2}$ can be realized in a bulk single crystal superlattice formed with an appropriate block layer. Correspondingly, we show that this material is a clean limit 2D superconductor exhibiting a BKT transition at $T_{BKT}$ = 0.82 K. The fundamental structural unit in hexagonal TMDs is the H-MX$_{2}$ layer where M and X are a transition metal and chalcogen, respectively. This structure breaks inversion symmetry in the layer plane owing to the trigonal prismatic coordination of X around M, and as a result yields an out-of-plane (Ising) spin-texture. For thin flakes deposited on substrates, the substrate-flake interface breaks mirror symmetry and yields an in-plane (Rashba) spin-texture. The simultaneous breaking of mirror and inversion symmetry leads to a mixed spin texture on the Fermi surface composed of both Ising and Rashba components. These spin-textures, and the resulting physics, are suppressed in the bulk limit where the overall unit cell preserves inversion symmetry. NMR experiments can be performed in order to elucidate the change in physical properties due to the symmetry breaking in the heterostructure. Varying the orientation of the applied magnetic field could allow us to clarify the effect of the symmetry breaking along the stacking direction. Furthermore, we could expose the main differences between bulk 2H-NbS$_{2}$ and monolayers of 1H-NbS$_{2}$ stacked onto the block layer. In conclusion, the combination of the transition metal dichalcogenide (TMD) superconductor 2H-niobium disulfide (2H-NbS$_{2}$) and the block layer provides a powerful example of high spin-orbit coupling effects which influence superconductivity and electronic transport properties.

### Robustness and invariance of entanglement in symmetry-protected topological phases at and away from the phase transition.

Fromholz, Pierre

Gapped topological phases of matter display exclusive entanglement properties that could prove useful in topological quantum computers. Much of these properties are unknown, in particular for symmetry-protected topological phases (SPTP). In my presentation, I will summarize a series a work (some of which I contributed to) that shows that the ground state of SPTP at low-dimension displays one long-range entanglement between the edge and that this entanglement can be extracted using the « disconnected entanglement entropy » SD. I show that this quantity is measurable (although with difficulties), that it is quantized, robust to disorder, and robust to quenches in the topological regime. I finally show that the quantity can be used at phase transition to obtain seemingly universal critical exponent, making SD a non-local analogous to an order parameter.

### Localization effects in the disordered two-dimensional Bose-Hubbard-model

Geißler, Andreas

In recent years experiments have shown localization effects consistent with the notion of many-body localization (MBL) for high-energy many-body states of the disordered Bose-Hubbard model in one and two-dimensional ultra-cold atomic lattice gases [1] as well as the related superfluid to Bose-glass ground state transition in three dimensions [2]. A proper theoretical understanding of MBL phenomena depends on knowledge about the full eigenstate spectrum. Therefore, exact numerical studies have been limited to small system sizes. In contrast, the Bose-glass phase can already be understood via the ground state [3]. So, by applying the fluctuation operator expansion method [4] to obtain beyond mean-field insight into the full fluctuation spectrum [3,5], I present the scaling analysis of both phenomena within a single framework. With the collection of obtained critical points, we are able to map out a phase diagram for the ground state and to characterize the mobility edge of the many-body quasiparticle excitations as extended and thermal. In the thermodynamic limit the shape of the mobility edge suggests the absence of a complete spectral localization transition. For a confined finite-size system, on the other hand, the method predicts a transition as observed in experiment as well a pattern dependence of the critical disorder strength at fixed energy density of the initial states. [1] C. D’Errico et al., PRL 113, 095301 (2014); J.-y. Choi et al., Science 352, 1547 (2016) [2] C. Meldgin et al., Nature Physics 12, 646 (2016) [3] A. Geissler, arXiv: 2011.10104 [4] A. Geissler et al., PRA 98, 063635 (2018) [5] A. Geissler, G. Pupillo, PRR 2, 042037 (2020)

### Higher-Order Weyl Semimetals

Ghorashi, Sayed Ali Akbar

### Criticality and phase diagram study of the long-range quantum Ising chain

Gonzalez Lazo, Eduardo

Zero-temperature and finite-temperature phase transitions of the quantum Ising chain are studied. Long-range (falling off as $1/r^\alpha$ , where $r$ is the distance between two spins in units of lattice spacing) ferromagnetic interaction among the spins are present in the model. This work characterize the critical behavior and phases for $\alpha=0.05$ and $\alpha=1.5$ using Path Integral Monte Carlo calculations. The thermodynamic limit behavior is studied applying Finite-Size-Scaling techniques to the obtained finite-sizes results. The results support the existence of a finite temperature transition for the studied values of $\alpha$, where the correlation length critical exponent has the same value through all the critical line.

### Composite Topological Structures in Superconductor-Ferromagnet Heterostructures

Görzen, Lucas

Magnet-superconductor hybrids are promising platforms that can allow the manipulation of topological defects of the superconducting order parameter by controlling the motion of structures in the magnetization field. We simulate the adiabatic motion of domain walls and magnetic vortices in a ferromagnetic thin film proximity-coupled to a superconducting layer hosting a superconducting vortex. The model assumption for the ferromagnetic layer is that the energy density contributions only consist of uniaxial anisotropy and exchange energy. Remarkably, we find that whether a superconducting vortex can be moved crucially depends on the chirality of the domain walls. Specifically Néel domain walls can \enquote{push} superconducting vortices. Magnetic vortex structures can generate spiral-like structures in the pairing potential of the superconductor if they exhibit a (counter) clockwise rotating magnetization. Furthermore, we apply and benchmark an efficient numerical method for the self-consistent calculation of the superconducting order parameter. Our method, based on Green’s functions in which the spectral density of non-interacting systems is approximated by Chebyshev polynomials, can drastically speed up the calculation for large system sizes and naturally lends itself to parallelization.

### Higher Order Auxiliary Field Quantum Monte Carlo Methods

Goth, Florian

The auxiliary field quantum Monte Carlo (AFQMC) method has been a workhorse in the field of strongly correlated electrons for a long time and has found its most recent implementation in the ALF package (alf.physik.uni-wuerzburg.de). The utilization of the Trotter decomposition to decouple the interaction from the non-interacting Hamiltonian makes this method inherently second order in terms of the imaginary time slice. We show that due to the use of the Hubbard-Stratonovich transformation (HST) a semigroup structure on the time evolution is imposed that necessitates the introduction of a new family of complex-hermitian splitting methods for the purpose of reaching higher order. We will give examples of these new methods and study their efficiency, as well as perform comparisons with other established second and higher order methods in the realm of the AFQMC method.

### Fluctuation control of non-thermal orbital orders

Grandi, Francesco

Multi-minima free energy surfaces represent many physical situations [1], such as different orbital orders in transition metal compounds. In this class of systems, fluctuations of the order parameters are essential in determining the shape of the free energy. Already at equilibrium, restoring forces are of entropic origin through the order-by-disorder mechanisms [2], and fluctuations can therefore be expected to be important for the nonequilibrium dynamics. This might open non-equilibrium pathways to control the dynamics of the order parameter and even stabilize states otherwise unstable at low temperatures [3]. Here, we describe the dynamics induced by suitable time-varying protocols in the 120° compass model using time-dependent Ginzburg-Landau theory [4], and we propose to use the momentum-resolved spectrum of the fluctuations to map out the instantaneous form of the potential, what should be soon achievable in time-resolved inelastic X-ray scattering experiments. One of the protocols we analyze is a time modulation of the exchange couplings that mimics the action of oscillating electric fields that have been suggested to modify the intensity of the exchange interactions for both orbital and spin degrees of freedom. In orbital models, this can lead to a force that acts directly on the order parameter and that can be used to switch the state of the system between equivalent configurations. We particularly study the interplay between this external force and the non-thermal entropic one during an orbital switching event. In the spirit of the control of non-thermal orders by light-manipulation of the fluctuations, we analyze a similar model that, in equilibrium, has a free energy that hosts several stable solutions and, above a critical temperature Tc, several metastable states induced by the order-by-disorder mechanism. After a sudden excitation of the fluctuations, we find it is possible to transiently stabilize the metastable state even if the temperature of the order parameter is below Tc. [1] Sun et al., Phys. Rev. X 10, 021028 (2020) [2] Nussinov et al., Rev. Mod. Phys. 87, 1 (2015) [3] Grandi and Eckstein, arXiv (2021) [4] Dolgirev et al., Phys. Rev. B 101, 174306 (2020)

### Momentum-resolved conductivity of strongly interacting bosons in optical lattice

Grygiel, Barbara

In recent years a significant progress in experimental techniques of trapping, cooling, and manipulating atomic gases has allowed for study of transport properties of these systems. In this talk I would like to present momentum-dependent conductivity of strongly interacting bosons in optical lattice. We use the Bose-Hubbard model in quantum rotor approach, which allows us to describe the superfluid-Mott insulator phase transition. Moreover, this approach takes into account the spatial fluctuations, thus it captures the influence of lattice geometry and spatially dependent gauge potentials. The conductivity is derived as a response function to a small, spatially non-uniform synthetic electric field. We present the momentum-resolved conductivity for square and cubic lattices both in the superfluid and Mott insulator phases. We also show that additional conductivity channels appear at non-zero temperature. The analysis of the conductivity in the case of uniformly filled lattice allows us to determine the group velocity of the excitation, which could provide a close link to experimental results.

### Possible inversion symmetry breaking in the $S=1/2$ pyrochlore Heisenberg magnet

Hagymasi, Imre

We address the ground state properties of the long-standing and much-studied three dimensional quantum spin liquid candidate, the $S=\frac 1 2$ pyrochlore Heisenberg antiferromagnet. By using $SU(2)$ DMRG, we are able to access cluster sizes of up to 128 spins. Our most striking finding is a robust spontaneous inversion symmetry breaking, reflected in an energy density difference between the two sublattices of tetrahedra, familiar as a starting point of earlier perturbative treatments. We also determine the ground state energy, $E_0/N_\text{sites} = -0.490(6) J$, by combining extrapolations of DMRG with those of a numerical linked cluster expansion. These findings suggest a scenario in which a finite-temperature spin liquid regime gives way to a symmetry-broken state at low temperatures.

### Information Dynamics in a Model with Hilbert Space Fragmentation

Hahn, Dominik

The fully frustrated ladder – a quasi-1D geometrically frustrated spin one half Heisenberg model –is non-integrable with local conserved quantities on rungs of the ladder, inducing the fragmentation of the Hilbert space into sectors composed of singlets and triplets on rungs. We explore the far-from-equilibrium dynamics of this model through the entanglement entropy and out-of-time-ordered correlators (OTOC). The post-quench dynamics of the entanglement entropy is highly anomalous as it shows clear non-damped revivals that emerge from short connected chunks of triplets and whose persistence is therefore a consequence of fragmentation. We find that the maximum value of the entropy follows from a picture where coherences between different fragments co-exist with perfect thermalization within each fragment. This means that the eigenstate thermalization hypothesis holds within all sufficiently large Hilbert space fragments. The OTOC shows short distance oscillations arising from short coupled fragments, which become decoherent at longer distances, and a sub-ballistic spreading and long distance exponential decay stemming from an emergent length scale tied to fragmentation.

### Fluctuations and symmetry effects in many body self-organization in a dissipative cavity

Halati, Catalin-Mihai

We investigate the full quantum evolution of ultracold interacting bosonic atoms on a chain and coupled to an optical cavity. Extending the time-dependent matrix product state techniques and the many-body adiabatic elimination techniques to capture the global coupling to the cavity mode and the open nature of the cavity, we examine the long time behavior of the system beyond the mean-field elimination of the cavity field. We show that the fluctuations beyond the mean-field state give a mixed state character to the dissipative phase transition and self-organized steady states. In the case of ideal bosons coupled to the cavity, the open system exhibits a strong symmetry which leads to the existence of conservation laws and multiple steady states. We find that the introduction of a weak breaking of the strong symmetry by a small interaction term leads to a direct transition from multiple steady states to a unique steady state.

### High magnetic field studies on atacamite, Cu$_2$Cl(OH)$_3$, a model compound for the $S = 1/2$ sawtooth chain

Heinze, Leonie

The mineral atacamite, Cu$_2$Cl(OH)$_3$, represents a model compound of the $S = 1/2$ sawtooth chain with both AFM couplings $J \sim 340$ K along the chain and $J' \sim 100$ K within the sawteeth, deduced from density functional theory [1]. We have extensively characterized the magnetic phase diagram of atacamite for ${\bf H} \parallel b$ axis: In low fields and below $T_{\rm N} = 8.4$ K a long-range ordered AFM state (propagation vector ${\bf q} = (1/2, 0, 1/2)$) is present [2]. Further, we have probed the high magnetic field region of the phase diagram by means of pulsed magnetic field measurements and have observed a flattening of the magnetization at $M = M_{\rm sat}/2$, which is entered for magnetic fields $> 31.5$ T [1]. We find that the flattening of the magnetization is unrelated to the known $1/2$-magnetization plateau of a quantum sawtooth chain, but might instead be understood as field-driven canting of a 3D network of weakly coupled sawtooth chains. [1] L. Heinze et al., arxiv:1904.07820 [cond mat.str el], [2] L. Heinze et al., Physica B 536, 377 (2018).

### Charge order from structured coupling in VSe2

Henke, Jans

Charge order - ubiquitous among correlated materials - is customarily described purely as an instability of the electronic structure. However, the resulting theoretical predictions often do not match high-resolution experimental data. A pertinent case is 1T-VSe2, whose single-band Fermi surface and weak-coupling nature make it qualitatively similar to the Peierls model underlying the traditional approach. Despite this, its Fermi surface is poorly nested, the thermal evolution of its charge density wave (CDW) ordering vectors displays an unexpected jump, and the CDW gap itself evades detection in direct probes of the electronic structure. We demonstrate that the thermal variation of the CDW vectors is naturally reproduced by the electronic susceptibility when incorporating a structured, momentum-dependent electron-phonon coupling, while the evasive CDW gap presents itself as a localized suppression of spectral weight centered above the Fermi level. Our results showcase the general utility of incorporating a structured coupling in the description of charge ordered materials, including those that appear unconventional. Ref: SciPost Phys. 9, 056 (2020). doi: 10.21468/SciPostPhys.9.4.056

### Real Space Classification of 2D Many-body Topological Phases

Herzog-Arbeitman, Jonah

The topological phases of non-interacting electrons have been exhaustively classified by their symmetries and spatial dimensions, culminating in a modern electronic band theory. More recently, a formalism using Real Space Invariants (RSIs) has enumerated the topological invariants in all 2D crystalline phases in terms of the Wannier functions which comprise the many-body groundstate. In this work, we generalize this classification to 2D interacting systems, and we find that interaction-stable topological phases are finite in number. We provide the topological invariants for each phase in terms of many-body RSIs for the 17 wallpaper groups with and without time-reversal symmetry and spin-orbit coupling, and connect the many-body RSIs to the band representation in the non- interacting limit. Our results show that all single-particle strong topology is stable to interactions. However, we find that some single-particle fragile phases may be trivialized, and we construct an analytically solvable interacting Hamiltonian which demonstrates this.

### Symmetry-enforced topological nodal planes at the Fermi surface of a chiral magnet

Hirschmann, Moritz

Topological semimetals and metals may contain nodal points or lines, i.e., zero- or one-dimensional crossings in the energy bands. In the present work we discuss an extension to two-dimensional nodal features. These nodal planes are enforced in systems described by certain nonsymmorphic space groups. We give criteria to predict nodal planes and consider in the process paramagnetic as well as magnetic space groups. Based on an analysis of symmetry eigenvalues we identify space groups with a necessarily non-zero Chern number associated to the nodal planes. The arguments are supported by minimal models and explicit calculation of the topological invariants. We have identified a number of materials with topological nodal planes, among them MnSi in its ferromagnetic phase.

### Dynamics of a Two-Dimensional Quantum Spin-Orbital Liquid: Spectroscopic Signatures of Fermionic Magnons

Hisano Natori, Willian Massashi

The coupling between spin and orbital degrees of freedom in Kugel-Khomskii models can enhance quantum fluctuations that prevent any spin-orbital order. The proposal of new systems that implement such Hamiltonians turns the computation of quantum spin-orbital liquids' signatures into a timely problem. In this talk, we discuss the exact dynamical correlations for the quantum spin-orbital liquid phases of an SU(2)-symmetric Kitaev honeycomb lattice model. This model is treated as a Hamiltonian of strongly interacting multiples of a j=3/2 total angular momentum. We show that the spin fractionalizes into S=1 fermionic magnons, whose dynamic correlation function can be analytically studied. We also show that the dynamical correlations of the total angular momentum can be exactly calculated using the same techniques developed to compute the S=1/2 Kitaev model's dynamics. We discuss how resonant inelastic x-ray scattering (RIXS) can uncover the fermionic magnons, while neutron scattering provides a mixed contribution of these particles and $Z_2$ gauge excitations. This work exemplifies how the phenomenology of quantum spin-orbital liquids differs from their spin-only counterparts, as well as the complementary roles of RIXS and INS in studying these systems.

### Magneto-thermodynamics of the $J_1$-$J_2$ Heisenberg antiferromagnet on the square lattice

Honecker, Andreas

We investigate the finite-temperature properties of the $J_1$-$J_2$ Heisenberg antiferromagnet on the square lattice in the presence of an external magnetic field. We focus on the highly frustrated regime around $J_2 \approx J_1/2$. The $H$-$T$ phase diagram is investigated with particular emphasis on the finite-temperature transition into the up-up-up-down'' state that is stabilized by thermal and quantum fluctuations and manifests itself as a plateau at one half of the saturation magnetization in the quantum case. Furthermore, we discuss the enhanced magnetocaloric effect associated to the ground-state degeneracy that arises at the saturation field for $J_2=J_1/2$. Computations for the spin-1/2 system are carried out using finite-temperature Lanczos and quantum typicality approaches.

### Fisher zeros and persistent coherence in M-qubit non-unitary quantum circuits

Hooley, Chris

We present a model of many-body quantum dynamics with measurements and post-selection that exhibits a panoply of space- and/or time-ordered phases, from ferromagnetic order to spin-density waves to time crystals. We demonstrate that these phases, including the inherently non-equilibrium dynamical ones, correspond to the complex-temperature equilibrium phases of the exactly solvable square-lattice anisotropic Ising model. Our results include: an explicit construction of the quantum circuit with local one- and two-spin gates; exact solutions onM-leg ladders that already exhibit decoherence-free subspaces that seed the 2D behavior; analytic continuation of the (partial) Onsager solution in the thermodynamic limit; numerical tensor network computations in the presence of an external magnetic field; and insights obtained using an exact fermionized solution.

### Characterization of strongly disordered many-body systems from one-particle measures

Hopjan, Miroslav

Typical experiments, designed to detect the many-body delocalization-localization transition, measure the dynamical properties of such systems [1]. However, much work has been done to provide evidence of the transition in the structure of eigenstates. In our recent works [2, 3], we introduce a new quantitative measure for the Fock-space localization [4], computed in the eigenstates. It has a distinct behaviour in the delocalized and localized phase, observed both for bosons [2] and fermions [3], and is potentially useful for the analysis of future experiments. Its scaling properties in the interacting systems are distinct from those in non-interacting systems [3] which points at a different mechanism for the transitions. Moreover, in fermionic systems, we extract a spatial subsystem entropy from the one-particle density matrix (OPDM) and observe that such entropy provides an upper bound on the entanglement entropy [5]. Interestingly, in the MBL regime, the OPDM entropy exhibits the main features of localization, i.e., the area law of eigenstates and the logarithmic growth with time after a quantum quench [5], and it thus provides an additional diagnostic tool for experiments. [1] See, e.g., Lukin et al. Science 364, 256 (2019), Choi et al, Science 352, 1547 (2016) [2] M. Hopjan and F. Heidrich-Meisner, Phys. Rev. A 101, 063617 (2020) [3] M. Hopjan, G. Orso and F. Heidrich-Meisner, in preparation [4] S. Bera, H. Schomerus, F. Heidrich-Meisner, and J. H. Bardarson, Phys. Rev. Lett. 115, 046603 (2015) [5] M. Hopjan, F. Heidrich-Meisner and V. Alba, arxiv:2011.02200 (2020)

### Dynamic Structure Factor of Disordered Coupled-Dimer Heisenberg models

Hörmann, Max

We investigate the impact of quenched disorder on the zero-temperature dynamic structure factor of coupled-dimer Heisenberg models on two-dimensional bilayers on the square, triangular and Kagome lattice. Using perturbative continuous unitary transformations, the effects on quasiparticles are investigated [1,2]. The disorder leads to intriguing quantum structures in dynamical correlation functions well observable in spectroscopic experiments. [1] M. Hörmann, P. Wunderlich, K. P. Schmidt, Phys. Rev. Lett. 121, 167201 (2018) [2] M. Hörmann and K. P. Schmidt, Physical Review B 102.9 (2020): 094427.

### Gutzwiller-projected trial states for quantum magnets at finite temperature

Horn, Friederike

Quantum gas microscopy can achieve single-site and spin-resolved detection of ultracold atoms in optical lattices. Being able to create such snapshots from a Hamiltonian provides an important link between theory and experiment. Here we propose a variational Monte Carlo method to sample the ground state of the 1D and 2D antiferromagnetic Heisenberg Hamiltonian at finite temperature. We construct a Gutzwiller projected density matrix from the eigenstates of a fermionic mean field approximation of the Heisenberg Hamiltonian. This enables us to compute the expectation value of the energy and approximate the entropy as a function of the mean fields and effective coupling constant. Minimizing the free energy we can thus obtain a variational ground state. We will present first results in a one dimensional system.

### Floquet driving enforced chiral hinge modes without quasi-energy gaps

Huang, Biao

We demonstrate in a 3D periodically driven model that an intricate type of chiral hinge mode shows up whose quasi-energy spectrum, surprisingly, fully mixes with the bulk spectrums. Such chiral modes exhibit robustness in a considerable range of Hamiltonian parameters and defect strengths. The existence and robustness of these chiral hinge modes can be traced back to an interplay between the boundary geometry and the peculiar bulk dispersions characteristic of a periodically driven system. A tentative topological theory is also formulated to describe such an unusual boundary mode living without quasi-energy gaps. As a by-product, the model we propose also coexists with a Floquet Weyl semimetal phase that can be straightforwardly realized in optical lattices. Ref: Biao Huang, Viktor Novičenko, André Eckardt, Gediminas Juzeliūnas, "Accumulation of chiral hinge modes and its interplay with Weyl physics in a three-dimensional periodically driven lattice system", arXiv:2101.08281

### Thermodynamics of the spin-half pyrochlore Heisenberg antiferromagnet

Hutak, Taras

The spin-half pyrochlore Heisenberg antiferromagnet (PHAF) is one of the most challenging problems in the field of highly frustrated quantum magnetism. We calculate thermodynamic properties of this model by interpolating between the low- and high-temperature behavior. For that, we follow ideas developed in detail by B.Bernu and G.Misguich [1] and use for the interpolation the entropy exploiting sum rules [the so-called entropy method (EM)]. We complement the EM results for the specific heat $c(T)$, the entropy $s(T)$, and the susceptibility $\chi(T)$ by the high-temperature expansion data up to order 13 [2]. The EM provides reliable data for the whole temperature region for the PHAF [3]. We do not find hints neither for an extra low-temperature peak nor an extra shoulder below the main maximum for $c(T)$. However, the absence of an extra low-temperature feature goes hand in hand with a significant shift of the single maximum towards $T\approx0.25$. A gapless spectrum is more favorable than a gapped one, i.e., most likely there is power-law low-temperature behavior of $c(T)$. Although best results are for an exponent $\alpha=2$, other exponents ($\alpha=1, 3/2, 5/2, 3$) cannot be excluded. We predict a ground-state energy $e_{0}\approx-0.52$. Our EM data for the susceptibility $\chi(T)$ in comparison with data obtained by diagrammatic Monte Carlo [4] provide further evidence for a gapless spectrum with a ground-state energy $e_{0}\approx-0.52$. We compare our findings with the ones obtained recently by other groups [5-7]. [1] B. Bernu and G. Misguich, Phys. Rev. B 63, 134409 (2001); G. Misguich and B. Bernu, Phys. Rev. B 71, 014417 (2005). [2] A. Lohmann, H.-J. Schmidt, and J. Richter, Phys. Rev. B 89, 014415 (2014). [3] O. Derzhko, T. Hutak, T. Krokhmalskii, J. Schnack, and J. Richter, Phys. Rev. B 101, 174426 (2020). [4] Y. Huang, K. Chen, Y. Deng, N. Prokof'ev, and B. Svistunov, Phys. Rev. Lett. 116, 177203 (2016). [5] R. Schäffer, I. Hagymási, R. Moessner, and D.J. Luitz, Phys. Rev. B 102, 054408 (2020). [6] I. Hagymási, R. Schäffer, R. Moessner, and D. J. Luitz, arXiv:2010.03563. [7] N. Astrakhantsev, T. Westerhout, A. Tiwari, K. Choo, A. Chen, M. H. Fischer, G. Carleo, and T. Neupert, arXiv:2101.08787.

### Towards a Topological Quantum Chemistry description of correlated systems: the case of the Hubbard diamond chain

Iraola, Mikel

The recently introduced topological quantum chemistry (TQC) framework has provided a description of universal topological properties of all possible band insulators in all space groups based on crystalline unitary symmetries and time reversal. While this formalism filled the gap between the mathematical classification and the practical diagnosis of topological materials, an obvious limitation is that it only applies to weakly interacting systems-which can be described within band theory. It is an open question to which extent this formalism can be generalized to correlated systems that can exhibit symmetry protected topological phases which are not adiabatically connected to any band insulator. In this work we address the many facettes of this question by considering the specific example of an extended version of a Hubbard diamond chain. This model features a Mott insulator, a trivial insulating phase and an obstructed atomic limit phase. Here we discuss the nature of the Mott insulator and determine the phase diagram and topology of the interacting model with infinite density matrix renormalization group calculations, variational Monte Carlo simulations and with many-body topological invariants. We then proceed by considering a generalization of the TQC formalism to Green's functions combined with the concept of topological Hamiltonian to identify the topological nature of the phases, using cluster perturbation theory to calculate the Green's functions. The results are benchmarked with the above determined phase diagram and we discuss the applicability and limitations of the approach and its possible extensions.

### Quantum critical points between spin liquids and long-range-ordered phases

Janssen, Lukas

Quantum spin liquids are exotic states of matter occurring in frustrated magnets. They feature fractionalized excitations interacting via an emergent gauge field and, in many cases, the absence of any long-range ordering. This makes their experimental or numerical identification a formidable task. On this poster, I argue that insight into the nature of putative quantum spin liquids can be gained by studying quantum phase transitions out of such states. In particular, I present an example of a quantum critical point between a U(1) Dirac spin liquid and a long-range-ordered phase, which we study using sign-problem-free quantum Monte Carlo simulations and a concomitant field-theoretical analysis. It will be shown that the presence of fractionalized excitations in the spin-liquid phase has significant consequences for the system's behavior near criticality. Quantum critical points adjacent to spin-liquid phases fall into novel fractionalized universality classes, the universal aspects of which will be discussed as well. Reference: [1] L. Janssen, W. Wang, M. M. Scherer, Z. Y. Meng, and X. Y. Xu, Confinement transition in the QED3-Gross-Neveu-XY universality class, Phys. Rev. B 101, 235118 (2020)

### Geometric Response of Chiral Superconductors

Jiang, Qingdong

Despite intense theoretical study and experimental effort, largely driven by possible applications in topological quantum computing, the most basic question about these materials - do they exist? - remains unsettled. This unsatisfactory situation arises because the experimental signatures which have been considered to date have proved either difficult to implement with sufficient precision, ambiguous to interpret, or both. Here we propose quantitatively clear and qualitatively striking signatures, based on geometric and dynamic generalizations of standard Josephson junctions, which could be decisive.

### Lightwave control of topological properties in 2D materials for sub-cycle and non-resonant valley manipulation

Jiménez-Galán, Alvaro

Modern light generation technology offers extraordinary capabilities for sculpting light pulses, with full control over individual electric field oscillations within each laser cycle [1]. These capabilities are at the core of lightwave electronics - the dream of ultrafast lightwave control over electron dynamics in solids, on a few-cycle to sub-cycle timescale, aiming at information processing at tera-Hertz to peta-Hertz rates. At the same time, quantum materials encompass fascinating properties such as the possibility to harness extra electronic degrees of freedom, e.g., the valley pseudospin [2]. Previous works have established optical initialization of the valley pseudospin via resonant circular pulses [3,4,5], taking advantage of the optical valley selection rules. Still, manipulating and reading the valley degree of freedom on timescales shorter than valley depolarization and in a non-material-specific (non-resonant) way, remains a crucial challenge. Bringing the frequency-domain concept of topological Floquet systems to the few-femtosecond time domain, I will present an all-optical, non-resonant approach to control the injection of carriers into the valleys on a few-femtosecond timescale by controlling the sub-cycle structure of non-resonant driving fields, and read the valley pseudospin in graphene-like monolayers by using the imprint of the Berry curvature on the high harmonic generation spectrum [6]. Such valley control does not rely on the optical valley selection rule. Instead, the tailored field modifies the laser-driven band structure on a sub-cycle timescale, allowing ultrafast optical control of the topological properties of 2D graphene-like quantum materials [7]. References [1] F. Krausz et al., Rev. Mod. Phys., 81 163 (2009). [2] S.A. Vitale et al., Small, 14 1801483 (2018). [3] D. Xiao et al., Phys. Rev. Lett., 99 236809 (2007). [4] F. Langer et al., Nature 557 76 (2018). [5] S.A. Oliaei Motlagh et al., Phys. Rev. B 100 115431 (2019). [6] R.E.F. Silva et al., Nat. Phot. 13 849 (2019). [7] Á. Jiménez-Galán et al., Nat. Phot. 14 728 (2020).

### Unsupervised machine learning of topological phase transitions from experimental data

Käming, Niklas

Recently, machine learning methods have been shown to be an alternative way of localizing phase boundaries also from noisy and imperfect data and without the knowledge of the order parameter. Using unsupervised machine learning techniques including anomaly detection and influence functions we obtain the topological phase diagram of the Haldane model in a completely unbiased fashion from experimental data. We show that the methods can successfully be applied to experimental data at finite temperature and to data of Floquet systems, when postprocessing the data to a single micromotion phase. Our work provides a benchmark for unsupervised detection of new exotic phases in complex many-body systems.

### Quantum droplet phases in extended Bose-Hubbard models with cavity-mediated interactions

Karpov, Peter

The Bose-Hubbard model and its various extensions have been studied for more than 30 years. We show that, surprisingly, there is still a room for new physics there, demonstrating a variety of quantum droplet phases. Such quantum droplets are self-bound objects which have recently drawn significant attention in continuum models featuring competing repulsive and attractive interactions and describing, for example, dipolar gases and bosonic mixtures. Multimode optical cavities offer an alternative, rapidly developing experimental platform, for studying competing short- and long-range interactions. Here, differently e.g. from the case of dipolar gases, the long-range cavity-mediated interaction can be widely tuned in range and strength. We study a system of bosonic atoms trapped in a lattice inside a multimode optical cavity, which can be modeled by an extended Bose-Hubbard model with competing on-site repulsive and finite-range (cavity-mediated) attractive interactions. We use the canonical worm Quantum Monte Carlo algorithm to explore the phase diagram of the model. Our approach is numerically exact and applicable in arbitrary dimensions. Moreover, since we explicitly work in the canonical ensemble, we don't have to fine-tune the chemical potential and can deal with arbitrary occupation numbers (up to the total number of particles in the system). Thus we can successfully study the droplet phases, overcoming the difficulties of other more conventional methods like grand-canonical worm algorithms, stochastic series expansion, and DMRG. The canonical worm algorithm can be straightforwardly applied to a more broad class of other experimentally relevant models featuring competing repulsive and attractive interactions, for example, dipolar gases and bosonic mixtures. In addition to the previously studied density-wave and supersolid self-organized superradiant phases, the finite-range cavity-mediated attraction can lead to the formation of quantum self-bound droplets. The droplet phases dominate the phase diagram and can include both compressible superfluid/supersolid as well as incompressible Mott and density-wave droplets.

### Confinement and Mott transitions of dynamical charges in 1D lattice gauge theories

Kebric, Matjaz

Lattice gauge theories (LGTs) have become a valuable tool to study strongly correlated condensed matter systems. This becomes in particular interesting when gauge degrees of freedom are coupled to matter since they allow us to study the complex problem of confinement. However, when the lattice is doped and matter becomes dynamical the clear notion of confinement becomes complicated. Here we study a one-dimensional (1D) \Zt LGT model where the gauge fields are coupled to dynamical charges with confining \Zt electric field and repulsive nearest-neighbour interactions. We map our model to a local string-length Hamiltonian where we link the confinement in the \Zt LGT model to a broken translational symmetry in the string-length basis. In addition we study the Mott transition of the charges at a specific filling of $n=2/3$. We find that the metallic phase of the confined Luttinger liquid is characterized by a hidden off-diagonal quasi-long-range order. Furthermore we map the 1D \Zt LGT model to a $t-J_{z}$ model which can be implemented in cold atom experiments by using the Rydberg dressing schemes; thus, we propose a way to directly test our theoretical predictions. https://arxiv.org/abs/2102.08375

### Statistical physics through the lens of real-space mutual information

Koch-Janusz, Maciej

Identifying the relevant coarse-grained degrees of freedom in a complex physical system is a key stage in developing powerful effective theories in and out of equilibrium. The celebrated renormalization group provides a framework for this task, but its practical execution in unfamiliar systems is fraught with ad hoc choices, whereas machine learning approaches, though promising, often lack formal interpretability. Recently, the optimal coarse-graining in a statistical system was shown to exist, based on a universal, but computationally difficult information-theoretic variational principle. This limited its applicability to but the simplest systems; moreover, the relation to standard formalism of field theory was unclear. Here we present an algorithm employing state-of-art results in machine-learning-based estimation of information-theoretic quantities, overcoming these challenges. We use this advance to develop a new paradigm in identifying the most relevant field theory operators describing properties of the system, going beyond the existing approaches to real-space renormalization. We evidence its power on an interacting model, where the emergent degrees of freedom are qualitatively different from the microscopic building blocks of the theory. Our results push the boundary of formally interpretable applications of machine learning, conceptually paving the way towards automated theory building.

### Discontinuous quantum and classical magnetic response of the pentakis dodecahedron

Konstantinidis, Nikolaos

The pentakis dodecahedron, the dual of the truncated icosahedron, consists of 60 edge-sharing triangles. It has 20 six- and 12 five-fold coordinated vertices, with the former forming a dodecahedron, and each of the latter connected to the vertices of one of the 12 pentagons of the dodecahedron. When spins mounted on the vertices of the pentakis dodecahedron interact according to the nearest-neighbor antiferromagnetic Heisenberg model, the two different vertex types necessitate the introduction of two exchange constants. As the relative strength of the two constants is varied the molecule interpolates between the dodecahedron and a molecule consisting only of quadrangles. The competition between the two exchange constants, frustration, and an external magnetic fi eld results in a multitude of ground-state magnetization and susceptibility discontinuities. At the classical level the maximum is ten magnetization and one susceptibility discontinuities when the 12 fi ve-fold vertices interact with the dodecahedron spins with approximately one-half the strength of their interaction. When the two interactions are approximately equal in strength the number of discontinuities is also maximized, with three of the magnetization and eight of the susceptibility. At the full quantum limit, where the magnitude of the spins equals 1/2, there can be up to three ground-state magnetization jumps that have the total $z$ spin component changing by $\Delta S^z = 2$, even though quantum fluctuations rarely allow discontinuities of the magnetization. The full quantum case also supports a $\Delta S^z = 3$ discontinuity. Frustration also results in nonmagnetic states inside the singlet-triplet gap. These results make the pentakis dodecahedron the molecule with the most discontinuous magnetic response from the quantum to the classical level.

### Tunable topological states hosted by unconventional superconductors with adatoms

Kreisel, Andreas

Chains of magnetic atoms, placed on the surface of s-wave superconductors, have been established as a laboratory for the study of Majorana bound states. In such systems, the breaking of time reversal due to magnetic moments gives rise to the formation of in-gap states, which hybridize to form one-dimensional topological superconductors. However, in unconventional superconductors even non-magnetic impurities induce in-gap states since scattering of Cooper pairs changes their momentum but not their phase. Here, we propose a realistic path for creating topological superconductivity, which is based on an unconventional superconductor with a chain of non-magnetic adatoms on its surface. The topological phase can be reached by tuning the magnitude and direction of a Zeeman field,such that Majorana zero modes at its boundary can be generated, moved and fused. To demonstrate the feasibility of this platform, we develop a general mapping of films with adatom chains to one-dimensional lattice Hamiltonians. This allows us to study unconventional superconductors such as Sr$_2$RuO$_4$ exhibiting multiple bands and an anisotropic order parameter.

### Kitaev quasiparticles in a proximate spin liquid: A many-body localization perspective.

Kumar, Aman

We study the stability of Kitaev quasiparticles in the presence of a perturbing Heisenberg interaction as a Fock space localization phenomenon. We identify parameter regimes where Kitaev states are localized, fractal, or delocalized in the Fock space of exact eigenstates, with the first two implying quasiparticle stability. Finite-temperature calculations show that a vison gap, and a nonzero plaquette Wilson loop at low temperatures, both characteristic of the deconfined Kitaev spin-liquid phase, persist far into the neighboring phase that has a concomitant stripy spin-density wave (SDW) order. The key experimental implication for Kitaev materials is that below a characteristic energy scale, unrelated to the SDW ordering, Kitaev quasiparticles are stable.

### Orbital Density Waves in Elemental Chalcogens

Stimulated by recent works highlighting the indispensable role of Coulomb interactions in the formation of helical chains and chiral electronic order in the elemental chalcogens, we explore the p-orbital Hubbard model on a one-dimensional helical chain. By solving it in the Hartree approximation we find a stable ground state with a period-three orbital density wave [1]. We establish that the precise form of the emerging order strongly depends on the Hubbard interaction strength. In the strong coupling limit, the Coulomb interactions support an orbital density wave that is qualitatively different from that in the weak-coupling regime. We identify the phase transition separating these two orbital ordered phases, and show that realistic values for the inter-orbital Coulomb repulsion in elemental chalcogens place them in the weak coupling phase, in agreement with observations of the order in the elemental chalcogens. [1] A. Klosinski, A. M. Oles, J. van Wezel and K. Wohlfeld, arxiv:2103.05925

### Anomalous Quantum Oscillations in a Heterostructure of Graphene on a Proximate Quantum Spin Liquid

Leeb, Valentin

The quasi two-dimensional Mott insulator $\alpha\text{-}{\text{RuCl}}_{3}$ is proximate to the sought-after Kitaev quantum spin liquid (QSL). In a layer of $\alpha\text{-}{\text{RuCl}}_{3}$ on graphene the dominant Kitaev exchange is further enhanced by strain. Recently, quantum oscillation (QO) measurements of such $\alpha\text{-}{\text{RuCl}}_{3}$ / graphene heterostructures showed an anomalous temperature dependence beyond the standard Lifshitz-Kosevich description. Here, we develop a theory of {\it anomalous QO} in an effective Kitaev-Kondo lattice model in which the itinerant electrons of the graphene layer interact with the correlated magnetic layer via spin interactions. At low temperatures a heavy Fermi liquid emerges such that the neutral Majorana fermion excitations of the Kitaev QSL acquire charge by hybridising with the graphene Dirac band. Using ab-initio calculations to determine the parameters of our low energy model we provide a microscopic theory of {\it anomalous QOs} with a non-LK temperature dependence consistent with our measurements. We show how remnants of fractionalized spin excitations can give rise to characteristic signatures in QO experiments.

### Influence matrix approach to quantum many-body dynamics

Lerose, Alessio

I will introduce an approach to study quantum many-body dynamics, inspired by the Feynman-Vernon influence functional. Its central object is the influence matrix (IM), which describes the effect of a Floquet many-body system on the dynamics of local subsystems. For translationally invariant systems, the IM obeys a self-consistency equation. For certain fine-tuned models, remarkably simple exact solutions appear, which represent perfect dephasers (PD), i.e., many-body systems acting as perfectly Markovian baths on their parts. Such PDs include dual-unitary quantum circuits investigated in recent works. In the vicinity of PD points, the system is not perfectly Markovian, but rather acts as a quantum bath with a short memory time. In this case, we demonstrate that the self-consistency equation can be solved using matrix-product states (MPS) methods, as the IM temporal entanglement is low. Using a combination of analytical insights and MPS computations, we characterize the structure of the IM in terms of an effective "statistical-mechanics" description for interfering intervals of local quantum trajectories and illustrate its predictive power by analytically deriving the relaxation rate of an impurity embedded in the system. In the last part of the talk, I will describe how to use these ideas to study the many-body localized (MBL) phase of strongly disordered interacting spin systems subject to periodic kicks. This approach allows to study exact disorder-averaged time evolution in the thermodynamic limit. MBL systems fail to act as efficient baths, and this property is encoded in their IM. I will discuss the structure of an MBL IM and link it to the onset of temporal long-range order.

### Large surface magnetization in noncentrosymmetric antiferromagnets

Lund, Mike Alexander

Thin-film antiferromagnets (AFs) with Rashba spin-orbit coupling are theoretically investigated. We demonstrate that the relativistic Dzyaloshinskii-Moriya interaction (DMI) produces a large surface magnetization and a boundary-driven twist state in the antiferromagnetic Néel vector. We predict a magnetization on the order of $2.3\times10^{4}$A/m, which is comparable to the magnetization of ferromagnetic semiconductors. Importantly, the magnetization is characterized by ultrafast terahertz dynamics and provides different approaches for efficiently probing and controlling the spin dynamics of AFs as well as detecting the antiferromagnetic DMI. Notably, the magnetization does not lead to any stray magnetic fields except at the corners where weak magnetic monopole fields appear.

### Shadow-band formation and recombination of optical excitations in a correlated band-insulator

Manmana, Salvatore R.

We study the time-evolution of single-particle spectral functions following an electron-hole excitation of a one-dimensional correlated band-insulator realized by a Hubbard model with a magnetic superlattice using matrix product states (MPS). For an excitation with a specified spin, we find the electron-electron interaction to induce recombination of the excitation by a spin-dependent redistribution of the weights. In the spin direction unaffected by the excitation, a shadow-band forms in the gap region. We compare this finding to the formation of excitons in extended Hubbard models without a superlattice.

### Bosonization of the Q= 0 continuum of Dirac fermions

Mantilla Serrano, Sebastián Felipe

We develop a bosonization formalism that captures non-perturbatively the interaction effects on the Q = 0 continuum of excitations of nodal fermions above one dimension. Our approach is a natural extension of the classic bosonization scheme for higher dimensional Fermi surfaces to include the Q = 0 neutral excitations that would be absent in a single-band system. The problem is reduced to solving a boson bilinear Hamiltonian. We establish a rigorous microscopic footing for this approach by showing that the solution of such boson bilinear Hamiltonian is exactly equivalent to performing the infinite sum of Feynman diagrams associated with the Kadanoff-Baym particle-hole propagator that arises from the self-consistent Hartree-Fock approximation to the single particle Green’s function. We apply this machinery to compute the interaction corrections to the optical conductivity of 2D Dirac Fermions with Coulomb interactions reproducing the results of perturbative renormalization group at weak coupling and extending them to the strong coupling regime.

### Bond Dependent Spin-Orbital Exchange and Quantum Order-by-Disorder in CoTiO3

McClarty, Paul

There has been a great deal of interest in bond-dependent anisotropic couplings in strong spin-orbit coupled magnets - especially iridates and ruthenates - that has brought new physics into focus. Recent theoretical work has proposed that such couplings can be significant in certain cobalt magnets where the spin-orbit coupling is sub-dominant [1]. Here we report on CoTiO3, an insulating ABC stacked honeycomb easy plane magnet that orders into a structure with ferromagnetic layers stacked antiferromagnetically with a spin wave spectrum that is known to host Dirac magnons [2]. Our high resolution inelastic neutron scattering data clearly shows the presence of a magnon gap of about 1meV that must arise through the presence of bond-dependent exchange couplings [3]. The spectral gap also provides strong evidence for the existence of a quantum order-by-disorder mechanism a very rare phenomenon that selects the long-ranged ordered magnetic structure through the effect of quantum fluctuations - that, in this material, crucially involves virtual crystal field excitations. The same couplings that lead to the spectral gap also cause the Dirac magnons to wind around one another in a double helix structure and we show that the experimental data is consistent with this scenario. We also show the presence of dispersive exciton modes with Dirac nodes. All the key features of the experiment are explicable through a multi-boson theory with spin-orbital exchange couplings. [1] H. Liu and G. Khaliullin, Phys. Rev. B 97, 014407 (2018); R. Sano, Y. Kato, and Y. Motome, Phys. Rev. B 97, 014408 (2018). [2] B. Yuan, I. Khait, G.-J. Shu, F. C. Chou, M. B. Stone, J. P. Clancy, A. Paramekanti, and Y.-J. Kim, Phys. Rev. X 10, 011062 (2020). [3] M. Elliot, P. A. McClarty, D. Prabhakaran, R. D. Johnson, H. C. Walker, P. Manuel, and R. Coldea, arXiv:2007.04199.

### Time evolution of terahertz-pumped heavy-fermion systems

Meirinhos, Francisco

Francisco Meirinhos and Johann Kroha Physikalisches Institut & Bethe Center for Theoretical Physics, Universität Bonn, Germany The search and characterisation of new quantum phases of matter has recently been intensified by the application of terahertz (THz) spectroscopy in the time domain to heavy-fermion systems [1-3]. It was experimentally shown that a single-cycle terahertz laser pulse disrupts the strongly correlated (Kondo) ground state in heavy-fermion compounds such as $CeCu_{6-x}Au_x$ which recovers after a characteristic delay time $\tau_K^*$, accompanied by the emission of a temporally confined terahertz echo pulse. In this way, time-domain terahertz spectroscopy provides direct access to both, the quasiparticle spectral weight and the characteristic time or energy scales, across a heavy-fermion quantum phase transition [1,2]. The transient nature of such non-equilibrium dynamics leads new and interesting many-body physics, raising questions about the established properties of quasi-particles. In the present work we develop the theoretical description of this heavy-fermion non-equilibrium dynamics. The electronic part of the system is represented by an Anderson model described by a time-dependent version of the non-equilibrium Non-Crossing Approximaton (NCA). The THz photons are treated as a quantum field with its own dynamics and coupled to the heavy fermion-system by a dipole interaction. In this way, incident THz pulses with arbitrary pulse shape can be implemented as an initial condition. At the same time, the photon quantum dynamics allows for re-emission of radiation and, thereby, the necessary release of energy during the relaxation dynamics to the heavy-fermion ground state. These coupled dynamics are solved by an efficient time-stepping algorithm. We also discuss the thermalisation to ambient temperature in terms of a Lindblad-like coupling to the electromagnetic environment as a bath. [1] C. Wetli, S. Pal, J. Kroha, K. Kliemt, C. Krellner, O. Stockert, H. v. Löhneysen, and M. Fiebig, Time-resolved collapse and revival of the Kondo state near a quantum phase transition, Nature Phys. {\bf 14}, 1103 (2018) [2] S. Pal, C. Wetli, F. Zamani, O. Stockert, H. v. Löhneysen, M. Fiebig, and J. Kroha, Phys. Rev. Lett. {\bf 122}, 096401 (2019) [3] C.-J. Yang, S. Pal, F. Zamani, K. Kliemt, C. Krellner, O. Stockert, H. v. Löhneysen, J. Kroha, and Manfred Fiebig, Phys. Rev. Research {\bf 2}, 033296 (2020)

### Unsupervised Learning Universal Critical Behavior via the Intrinsic Dimension

Mendes Santos, Tiago

The identification of universal properties from minimally processed data sets is one goal of machine learning techniques applied to statistical physics. Here, we study how the minimum number of variables needed to accurately describe the important features of a data set - the intrinsic dimension (ID) - behaves in the vicinity of phase transitions. We employ state-of-the-art nearest-neighbors-based ID estimators to compute the ID of raw Monte Carlo thermal configurations across different phase transitions: first-order, second-order, and Berezinskii-Kosterlitz-Thouless. For all the considered cases, we find that the ID uniquely characterizes the transition regime. The finite-size analysis of the I d allows us to not only identify critical points with an accuracy comparable to methods that rely on a priori identification of order parameters but also to determine the corresponding (critical) exponent $\nu$ in the case of continuous transitions. For the case of topological transitions, this analysis overcomes the reported limitations affecting other unsupervised learning methods. Our work reveals how raw data sets display unique signatures of universal behavior in the absence of any dimensional reduction scheme and suggest direct parallelism between conventional order parameters in real space and the intrinsic dimension in the data space.

### From black holes to Weyl semimetals

Meng, Tobias

Weyl semimetals are a recent example of solid state materials featuring a relativistic band structure. This analogy has lead to the intriguing proposal that Weyl semimetals can mimic various effects known from high energy physics, such as Klein tunnelling. In this talk, I will discuss how Weyl semimetals with (over-)tilted nodes connect to black hole matrices, and what experimentally observable consequences thereof are.

### Improved quantum transport calculations for interacting nanostructures

Minarelli, Emma

Nanoelectronics devices such as semiconductor quantum dots and single molecule transistors exhibit a rich range of physical behavior due to the interplay between orbital complexity, strong electronic correlations and device geometry. Understanding and simulating the quantum transport through such nanostructures is essential for rational design and technological applications. In this talk, I will discuss both electric and heat quantum transport for interacting mesoscopic quantum transport. For the electric conductance, calculations are developed under linear response and I demonstrate the improvement over standard methods with applications such as triple quantum dots and two-channel charge Kondo models using the numerical renormalization group technique (NRG). I will treat reformulations of the Meir-Wingreen formula in the context of non-proportionate coupling set-ups and by means of perturbative verification of the Ng ansatz; of the Oguri formula in non-Fermi Liquid states and of the Kubo formula for conductance. For the heat conductance, both non-equilibrium versus linear response formulation are discussed, in particular with respect to their viability using NRG.

### Electrical conductivity formulas for a general two-band model and their application

Mitscherling, Johannes

In recent years, there is an increasing interest in transport properties of multiband systems due to advances in experimental techniques. We focus on the longitudinal, the anomalous and the ordinary Hall conductivity for a general two-band model. This model captures a broad spectrum of systems with very different and rich physics like Chern insulators, ferromagnets, and spiral spin density waves. We will see in a simple and fundamental derivation how two criteria for a unique and physically motivated decomposition of the conductivity formulas naturally arise from the multiband structure of the model. Those criteria allow us to relate interband contributions to concepts of quantum geometry, namely the quantum metric and the Berry curvature. They lead to a decomposition whose individual scaling behaviors with respect to the scattering rate can be analyzed systematically. We exemplify the general analysis by several applications ranging from spiral magnetic order in cuprates to the quantum anomalous Hall effect in Chern insulators.

### Interaction-stabilized topological magnon insulator in ferromagnets

Mook, Alexander

Condensed matter systems admit topological collective excitations above a trivial ground state, an example being Chern insulators formed by Dirac bosons with a gap at finite energies. However, in contrast to electrons, there is no particle-number conservation law for collective excitations. This gives rise to particle number-nonconserving many-body interactions whose influence on single-particle topology is an open issue of fundamental interest in the field of topological quantum materials. Taking magnons in ferromagnets as an example, we uncover topological magnon insulators that are stabilized by interactions through opening Chern-insulating gaps in the magnon spectrum. This can be traced back to the fact that the particle-number nonconserving interactions break the effective time-reversal symmetry of the harmonic theory. Hence, magnon-magnon interactions are a source of topology that can introduce chiral edge states, whose chirality depends on the magnetization direction. Importantly, interactions do not necessarily cause detrimental damping but can give rise to topological magnons with exceptionally long lifetimes. We identify two mechanisms of interaction-induced topological phase transitions and show that they cause unconventional sign reversals of transverse transport signals, in particular of the thermal Hall conductivity. Our results demonstrate that interactions can play an important role in generating nontrivial topology. Reference: Alexander Mook, Kirill Plekhanov, Jelena Klinovaja, Daniel Loss, arXiv:2011.06543 (2020)

### Phase coherence in out-of-equilibrium supersolid states of ultracold dipolar atoms

Morpurgo, Giacomo

A supersolid is a counterintuitive phase of matter that combines the global phase coherence of a superfluid with a crystal-like self-modulation in space. Recently, such states have been experimentally realized using dipolar quantum gases. Here we investigate the response of a dipolar supersolid to an interaction quench that shatters the global phase coherence. We identify a parameter regime in which this out-of-equilibrium state rephases, indicating superfluid flow across the sample as well as an efficient dissipation mechanism. We find a crossover to a regime where the tendency to rephase gradually decreases until the system relaxes into an incoherent droplet array. Although a dipolar supersolid is, by its nature, ‘soft’, we capture the essential behaviour of the de- and rephasing process within a rigid Josephson junction array model. Yet, both experiment and simulation indicate that the interaction quench causes substantial collective mode excitations that connect to phonons in solids and affect the phase dynamics.

### Competition between X-Cube and Toric Code in three dimensions

Mühlhauser, Matthias

We investigate the competition of the X-Cube model with the 3D Toric code using variational mean-field calculations and high-order series expansions. We determine the complete phase diagram, which interestingly consists of four regions, i.e. apart from the topologically ordered toric code phase and the X-Cube fracton phase we find two regions which are adiabatically connected to classical spin-liquid phases. In the end we also investigate the effect of an additional magnetic field in x- or z-direction using variational mean-field calculations.

### Anyonic Molecules in Atomic Fractional Quantum Hall Liquids: A Quantitative Probe of Fractional Charge and Anyonic Statistics

Muñoz de las Heras, Alberto

We study the quantum dynamics of massive impurities embedded in a strongly interacting, two-dimensional atomic gas driven into the fractional quantum Hall (FQH) regime under the effect of a synthetic magnetic field. For suitable values of the atom-impurity interaction strength, each impurity can capture one or more quasihole excitations of the FQH liquid, forming a bound molecular state with novel physical properties. An effective Hamiltonian for such anyonic molecules is derived within the Born-Oppenheimer approximation, which provides renormalized values for their effective mass, charge, and statistics by combining the finite mass of the impurity with the fractional charge and statistics of the quasiholes. The renormalized mass and charge of a single molecule can be extracted from the cyclotron orbit that it describes as a free particle in a magnetic field. The anyonic statistics introduces a statistical phase between the direct and exchange scattering channels of a pair of indistinguishable colliding molecules and can be measured from the angular position of the interference fringes in the differential scattering cross section. Implementations of such schemes beyond cold atomic gases are highlighted—in particular, in photonic systems.

### Conductivity and thermoelectric coefficients of doped SrTiO$_3$ at high temperatures

Nazaryan, Khachatur

We developed a theory of electric and thermoelectric conductivity of lightly doped SrTiO$_3$ in the non-degenerate region $k_B T \geq E_F$, assuming that the major source of electron scattering is their interaction with soft transverse optical phonons present due to proximity to ferroelectric transition. We have used kinetic equation approach within relation-time approximation and we have determined energy-dependent transport relaxation time $\tau(E)$ by the iterative procedure. Using electron effective mass $m$ and electron-transverse phonon coupling constant $\lambda$ as two fitting parameters, we are able to describe quantitatively a large set of the measured temperature dependences of resistivity $R(T)$ and Seebeck coefficient $\mathcal{S}(T)$ for a broad range of electron densities studied experimentally in recent paper. In addition, we calculated Nernst ratio $\nu=N/B$ in the linear approximation over weak magnetic field in the same temperature range.

### Orbital magnetic moment of magnons

Neumann, Robin

It is commonly accepted that magnons---collective excitations in a magnetically ordered system---carry a spin of $1\hbar$ or, phrased differently, a magnetic moment of $g \mu_\text{B}$. In this talk, I demonstrate that magnons carry magnetic moment beyond their spin magnetic moment. Our rigorous quantum theory uncovers a magnonic orbital magnetic moment brought about by spin-orbit coupling. We apply our theory to two paradigmatic systems where the notion of orbital moments manifests itself in novel fundamental physics rather than just quantitative differences. In a coplanar antiferromagnet on the two-dimensional kagome lattice the orbital magnetic moment gives rise to an orbital magnetization. While the spin magnetization is oriented in the kagome plane, the orbital magnetization also has a finite out-of-plane component leading to orbital weak ferromagnetism.'' The insulating collinear pyrochlore ferromagnet Lu$_2$V$_2$O$_7$ exhibits a magnonic orbital Nernst effects,'' i.\,e. transversal currents of orbital magnetic moment induced by a temperature gradient. The orbital magnetization and the orbital Nernst effect in magnetic insulators are two signatures of the orbital magnetic moment of magnons.

### Special states in quantum many-body spectra

Nielsen, Anne

Exceptions to thermalization in quantum many-body systems provide interesting opportunities. Many-body localization, in which all states in the spectrum have area law entanglement, constitutes a strong violation of the eigenstate thermalization hypothesis, and quantum many-body scars instead give rise to a weak violation with a few nonthermal states embedded in a spectrum of thermal states. Here, we propose and demonstrate that one can similarly have a weak violation of many-body localization, in which one or a few states in a spectrum have above area law entanglement, while the rest of the states are many-body localized. We show that this can be achieved through a mechanism, in which emergent symmetry of the special states prevents many-body localization in these states. Reference: Phys. Rev. Lett. 125, 240401 (2020)

### Bosonic Pfaffian State in the Hofstadter-Bose-Hubbard Model

Palm, Felix A.

Topological states of matter, such as fractional quantum Hall states, are an active field of research due to their exotic excitations. In particular, ultracold atoms in optical lattices provide a highly controllable and adaptable platform to study such new types of quantum matter. However, finding a clear route to realize non-Abelian quantum Hall states in these systems remains challenging. Here we use the density-matrix renormalization-group (DMRG) method to study the Hofstadter-Bose-Hubbard model at filling factor $\nu=1$ and find strong indications that at $\alpha=1/6$ magnetic flux quanta per plaquette the ground state is a lattice analog of the continuum non-Abelian Pfaffian. We study the on-site correlations of the ground state, which indicate its paired nature at $\nu=1$, and find an incompressible state characterized by a charge gap in the bulk. We argue that the emergence of a charge density wave on thin cylinders and the behavior of the two- and three-particle correlation functions at short distances provide evidence for the state being closely related to the continuum Pfaffian. The signatures discussed here are accessible in current cold atom experiments and we show that the Pfaffian-like state is readily realizable in few-body systems using adiabatic preparation schemes.

### Boundary Critical Behavior of the Three-Dimensional Heisenberg Universality Class

Parisen Toldin, Francesco

We study the boundary critical behavior of the three-dimensional Heisenberg universality class, in the presence of a bidimensional surface. By means of high-precision Monte Carlo simulations of an improved lattice model, where leading bulk scaling corrections are suppressed, we prove the existence of a special phase transition, with unusual exponents, and of an extraordinary phase with logarithmically decaying correlations. These findings contrast with naive arguments on the bulk-surface phase diagram, and allow us to explain some recent puzzling results on the boundary critical behavior of quantum spin models. Ref: F. Parisen Toldin, arXiv:2012.00039, Phys. Rev. Lett. (2021), to be published

### Finite frequency backscattering current noise at a helical edge

Pashinsky, Boris

Magnetic impurities with sufficient anisotropy could account for the observed strong deviation of the edge conductance of 2D topological insulators from the anticipated quantized value. In this work we consider such a helical edge coupled to dilute impurities with an arbitrary spin S and a general form of the exchange matrix. We calculate the backscattering current noise at finite frequencies as a function of the temperature and applied voltage bias. We find that, in addition to the Lorentzian resonance at zero frequency, the backscattering current noise features Fano-type resonances at nonzero frequencies. The widths of the resonances are controlled by the spectrum of corresponding Korringa rates. At a fixed frequency the backscattering current noise has nonmonotonic behavior as a function of the bias voltage.

### A quantum Boltzmann equation for strongly correlated electrons

Picano, Antonio

Collective orders and photo-induced phase transitions in quantum matter can evolve on timescales which are orders of magnitude slower than the femtosecond processes related to electronic motion in the solid. Quantum Boltzmann equations can potentially resolve this separation of timescales, but are often constructed within a perturbative framework. Here we derive a quantum Boltzmann equation which only assumes a separation of timescales (taken into account through the gradient approximation for convolutions in time), but is based on a non-perturbative scattering integral, and makes no assumption on the spectral function such as the quasiparticle approximation. In particular, a scattering integral corresponding to non-equilibrium dynamical mean-field theory is evaluated in terms of an Anderson impurity model in a non-equilibrium steady state with prescribed distribution functions. This opens the possibility to investigate dynamical processes in correlated solids with quantum impurity solvers designed for the study of non-equilibrium steady states.

### Prethermal phases of matter in dimension 1, 2, and 3

Pizzi, Andrea

Many-body systems under a high-frequency drive spend an exponentially long time in a prethermal regime. The recent investigation of this regime for the realization of novel prethermal phases of matter has been severely limited by the computational challenges associated with the exponentially large Hilbert space of quantum many-body systems. We explore prethermal phases of matter in classical many-body systems undergoing driven Hamiltonian dynamics in one, two and three dimensions. First, we show that the phenomenology of known 1D quantum prethermal phases of matter is virtually the same when going classical, which suggests that these phenomena should in essence be thought of as robust to quantum fluctuations, rather than dependent on them. Second, we make use of efficient classical simulations to study the interplay between dimensionality and interaction range. For instance, we show that, in contrast to 1D, nontrivial prethermal phases can emerge in 3D even in short-range interacting systems. As concrete examples, we focus on higher-order and fractional discrete time crystals, prethermal phases of matter breaking the time translational symmetry of a drive with unexpectedly large and possibly fractional periods. Our work paves the way towards the study of novel prethermal phases of matter beyond the (few) known one-dimensional examples.

### Yu-Shiba-Rusinov states of single magnetic molecule in an s−wave superconductor

We use the numerical renormalization group theory to investigate the Yu-Shiba-Rusinov (YSR) bound state properties of single magnetic molecules placed in an s-wave superconducting substrate. The molecule consists of a large core spin and a single orbital, coupled via exchange interaction. The critical Coulomb interaction for the singlet/doublet transition decreases in the presence of this exchange interaction for both Ferro and anti-ferromagnetic couplings. The number of YSR states also increases to two pairs, however, in the singlet phase, one of the pairs has zero spectral weight. We explore the evolution of the in-gap states using the Anderson model. Away from the particle-hole symmetry point, the results suggest a doublet-singlet-doublet transition as the on-site energy is lowered while keeping the Coulomb interaction fixed. To understand these results, we write down an effective model for the molecule in the limit of a large superconducting order parameter. Qualitatively, it explains the various phase transitions and spectral nature of the in-gap states.

### Doping a Topological Insulator

Rachel, Stephan

The search for topological superconductors is one of the most pressing and challenging questions in condensed matter and material research. Despite some early suggestions that "doping a topological insulator" might be a successful recipe to find topological superconductors, until today there is no general understanding of the relationship of the topology of the superconductor and the topology of its underlying normal state system. One of the major obstacles is the strong effect of the Fermi surface and the subsequent pairing tendencies, usually preventing a detailed analysis and comparison between different topological superconducting systems. Here we present an analysis of doped topological insulators where the dominant Fermi surface effects have been removed. Our approach allows us to study and compare superconducting instabilities of different insulating normal state systems and reveal the potential of doping a topological insulator.

### Non-equilibrium evolution of Bose-Einstein condensate deformation in temporally controlled weak disorder

We consider a time-dependent extension of a perturbative mean-field approach to the homogeneous dirty boson problem by considering how switching on and off a weak disorder potential affects the stationary state of an initially equilibrated Bose-Einstein condensate by the emergence of a disorder-induced condensate deformation. We find that in the switch on scenario the stationary condensate deformation turns out to be a sum of an equilibrium part [1], that actually corresponds to adiabatic switching on the disorder, and a dynamically-induced part, where the latter depends on the particular driving protocol [2]. If the disorder is switched off afterwards, the resulting condensate deformation acquires an additional dynamically-induced part in the long-time limit, while the equilibrium part vanishes. We also present an appropriate generalization to inhomogeneous trapped condensates. Our results demonstrate that the condensate deformation represents an indicator of the generically non-equilibrium nature of steady states of a Bose gas in a temporally controlled weak disorder. [1] K. Huang and H.-F. Meng, Phys. Rev. Lett. 69, 644 (1992) [2] Milan Radonjić and Axel Pelster, SciPost Phys. 10, 008 (2021)

### Finite temperature phase diagram of ultracold bosons in a two-dimensional optical Hubbard lattice

Ray, Sayak

The Bose-Hubbard model (BHM) is well celebrated for its success to describe the phases and dynamics of ultracold interacting bosons in an optical lattice. In this work we compute the equilibrium phase diagram of the BHM at finite temperature using the cluster mean field (CMF) theory and show that this method is capable of describing the phase boundary accurately in good agreement with previous quantum Monte Carlo (QMC) studies as well with experiments. We calculate the condensate density in the superfluid (SF) phase, vanishing of which indicates the SFto- normal-fluid (NF) phase boundary. The compressibility, involving particle-hole excitations, is calculated in the SF, NF and Mott insulator phases. It provides an estimate of the crossover temperature from the MI to the NF state. Our method offers an advantage to analyze the effect of correlations systematically with increasing cluster size followed by a finite-cluster-size scaling, and at the same time overcomes the low temperature difficulties of QMC. Ulli Pohl, Sayak Ray, and Johann Kroha Physikalisches Institut, Rheinische Friedrich-Wilhelms-Universität Bonn, Nußallee 12, 53115, Bonn, Germany

### Fracton excitations in classical frustrated kagome spin models

Reuther, Johannes

Fractons are topological quasiparticles with limited mobility. While there exists a variety of models hosting these excitations, typical fracton systems require rather complicated many-particle interactions. Here, we discuss fracton behavior in the more common physical setting of classical kagome spin models with frustrated two-body interactions only. We investigate systems with different types of elementary spin degrees of freedom (three-state Potts, XY, and Heisenberg spins) which all exhibit characteristic subsystem symmetries and fracton-like excitations. The mobility constraints of isolated fractons and bound fracton pairs in the three-state Potts model are, however, strikingly different compared to the known type-I or type-II fracton models. One may still explain these properties in terms of type-I fracton behavior and construct an effective low-energy tensor gauge theory when considering the system as a 2D cut of a 3D cubic lattice model. Our extensive classical Monte-Carlo simulations further indicate a crossover into a low temperature glassy phase where the system gets trapped in metastable fracton states. Moving on to XY spins, we find that in addition to fractons the system hosts fractional vortex excitations. As a result of the restricted mobility of both types of defects, our classical Monte-Carlo simulations do not indicate a Kosterlitz-Thouless transition but again show a crossover into a glassy low-temperature regime. Finally, the energy barriers associated with fractons vanish in the case of Heisenberg spins, such that defect states may continuously decay into a ground state. These decays, however, exhibit a power-law relaxation behavior which leads to slow equilibration dynamics at low temperatures.

### Generative Model Learning For Molecular Electronics

Rigo, Jonas

The use of single-molecule transistors in nanoelectronics devices requires a deep understanding of the generalized'quantum impurity'models describing them. Microscopic models comprise molecular orbital complexity and strong electron interactions while also treating explicitly conduction electrons in the external circuit. No single theoretical method can treat the low-temperature physics of such systems exactly. To overcome this problem, we use a generative machine learning approach to formulate effective models that are simple enough to be treated exactly by methods such as the numerical renormalization group, but still capture all observables of interest of the physical system. We illustrate the power of the new methodology by application to the single benzene molecule transistor.

### Analysis of electronic properties of twisted bilayer graphene using exact diagonalization

Rodrigues, Alina

Twisted bilayer graphene (TBG), a structure created through the misalignment of two graphene sheets stacked one on top of the other, became an object of a great interest due to strong electronic correlations present in these systems [1-2]. The source of the correlations has not yet been explained, however its consequences were noticed in the experiments, where insulating and superconducting states were observed [3-4]. A significant effort is now being put into understanding the nature of these correlations [5-6]. Presented results are based on the exact diagonalization (ED) method which allows for precise analysis of the electronic correletions. It is however limited to small system studies. In our research an extension of the ED method was applied that truncates the dimension of the Hilbert space through dismissing electron configurations that have relatively small diagonal element in the Hamiltonian. We have analysed different system sizes and electron configurations. [1] J. M. B. Lopes dos Santos, N. M. R. Peres, A. H. Castro Neto, Phys. Rev. Lett. 99, 256802 (2007)\\ [2] E. Bistritzer and Allan H. MacDonald, PNAS 108, 12233 (2011)\\ [3] Y. Cao, V. Fatemi, A. Demir, S. Fang, S. L. Tomarken, J. Y. Luo, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, E. Kaxiras, R. C. Ashoori \& P. Jarillo-Herrero, Nature 556, 80 (2018)\\ [4] Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras \& P. Jarillo-Herrero, Nature 556, 43 (2018)\\ [5] M. Koshino, N. F. Q. Yuan, T. Koretsune, M. Ochi, K. Kuroki, and L. Fu, Phys. Rev. X 8, 031087 (2018)\\ [6] J. F. Dodaro, S. A. Kivelson, Y. Schattner, X. Q. Sun, and C. Wang, Phys. Rev. B 98, 075154 (2018)\\

### Metastability in open quantum systems

Rose, Dominic

We expand on a recently developed theory for metastability in open quantum systems to allow for the understanding and analysis of emergent classical metastability. We first develop the theory required to measure the accuracy of a classical approximation to a generic quantum dynamics at long-times. We then use this theory to construct a general algorithmic approach to finding a good classical approximation to this long-time dynamics. We apply this theory to two systems; an open quantum Ising model and an open quantum generalization of the glassy East model. These exhibit strongly intermittent emission dynamics characteristic of systems with competing dynamical phases. We show that for appropriate parameters these systems dynamics display pronounced metastability, i.e., the system relaxes first to long-lived metastable states, before eventual relaxation to the true stationary state. From the spectral properties of the quantum master operator we characterise the low-dimensional manifold of metastable states for these models. We show that the long time dynamics can be accurately approximated by a classical stochastic dynamics between the metastable phases, directly related to the intermittent dynamics observed in quantum trajectories. In particular we demonstrate that the effective dynamics between the metastable states of the quantum East model is simply an adjustment of the long-time dynamics of the classical East model.

### Magnon driven bidirectional domain wall motion in kagome antiferromagnets

Salimath, Akshaykumar

Antiferromagnet based insulator spintronics is emerging as a revolution in quest for next generation ultra-low power technologies. In metallic spintronics, the physical moment of electrons contributes towards joule heating. In contrast, in antiferromagnet insulators, spin information is carried by magnetic excitations called magnons resulting in ultra-low power information transfer and processing. Antiferromagnets are abundant in nature and are associated with much richer physics. Recently, a class of non-collinear antiferromagnets with kagome lattice structure have garnered significant interest due to their inherent magnetic frustration. The large exchange interaction in these materials result in resonance frequencies in several THz range. For their ultimate applications in spintronics as an active layer, it is important to understand efficient manipulation of magnetic textures in these materials. In this work, we gain numerical and theoretical insights into the magnon dispersion bands in 1D kagome antiferromagnets, followed by magnon driven dynamics of domain wall. We observe that the domain wall can be efficiently manipulated by y-polarized spin waves in these materials. Remarkably, in our simulations, we observe bidirectional domain wall motion by tuning the frequency of the spin waves around the non-dispersive magnon band. The simulations are performed in our homegrown atomistic LLG solver. We substantiate the results through analytics derived from the Lagrangian formalism. The scattering of the magnons near the flat band which result in domain wall motion away from the source can be explained through WKB approximation, while the reflectionless behavior away from the flat band which result in domain wall motion towards the source can be explained with modified Po ̈schl-Teller potential problem. Our results are particularly interesting for racetrack memory applcations owing to the fact that we can control the direction of the information bits just by varying the frequency of the source rather than the polarity.

### Quantum Monte Carlo simulation of generalized Kitaev models

Sato, Toshihiro

We introduce a phase pinning approach in the realm of the auxiliary field quantum Monte Carlo algorithm for the generalized Kitaev model. This phase pinning strategy greatly reduces the severity of the negative sign problem and opens a window of temperatures relevant to experiments where exact quantum Monte Carlo simulations can be carried out. We demonstrate this by carrying out extensive simulations of thermodynamical and dynamical properties of the Kitaev-Heisenberg model. Our numerical data reveals finite temperature properties of ordered and Kitaev spin-liquid phases inherent to the Kitaev-Heisenberg model.

### Pyrochlore $S=\frac{1}{2}$ Heisenberg antiferromagnet at finite temperature

Schäfer, Robin

We use a combination of three computational methods to investigate the notoriously difficult frustrated three dimensional pyrochlore $S=1/2$ quantum antiferromagnet, at finite temperature, $T$: canonical typicality for a finite cluster of $2\times 2 \times 2$ unit cells (i.e. $32$ sites), a finite-$T$ matrix product state method on a larger cluster with $48$ sites, and the numerical linked cluster expansion (NLCE) using clusters up to $25$ lattice sites, including non-trivial hexagonal and octagonal loops. We calculate thermodynamic properties (energy, specific heat capacity, entropy, susceptibility, magnetization) and the static structure factor. We find a pronounced maximum in the specific heat at $T = 0.57 J$, which is stable across finite size clusters and converged in the series expansion. At $T\approx 0.25J$ (the limit of convergence of our method), the residual entropy per spin is $0.47 k_B \ln2$, which is relatively large compared to other frustrated models at this temperature. We also observe a non-monotonic dependence on $T$ of the magnetization at low magnetic fields, reflecting the dominantly non-magnetic character of the low-energy states. A detailed comparison of our results to measurements for the $S=1$ material NaCaNi$_2$F$_7$ yields a rough agreement of the functional form of the specific heat maximum, which in turn differs from the sharper maximum of the heat capacity of the spin ice material Dy$_2$Ti$_2$O$_7$.

### From observations to complexity of quantum states via unsupervised learning

Schmitt, Markus

The vast complexity is a daunting property of generic quantum states that poses a significant challenge for theoretical treatment, especially for non-equilibrium setups. Therefore, it is vital to recognize states which are locally less complex and thus describable with (classical) effective theories. We use unsupervised learning with autoencoder neural networks to detect the local complexity of time-evolved states by determining the minimal number of parameters needed to reproduce local observations. The latter can be used as a probe of thermalization, to assign the local complexity of density matrices in open setups and for the reconstruction of underlying Hamiltonian operators. Our approach is an ideal diagnostics tool for data obtained from (noisy) quantum simulators because it requires only practically accessible local observations.

### Fine-Grained Tensor Network Methods

Schmoll, Philipp

We develop a strategy for tensor network algorithms that allows to deal very efficiently with lattices of high connectivity. The basic idea is to fine-grain the physical degrees of freedom, i.e., decompose them into more fundamental units which, after a suitable coarse-graining, provide the original ones. Thanks to this procedure, the original lattice with high connectivity is transformed by an isometry into a simpler structure, which is easier to simulate via usual tensor network methods. In particular this enables the use of standard schemes to contract infinite 2d tensor networks - such as Corner Transfer Matrix Renormalization schemes - which are more involved on complex lattice structures. We prove the validity of our approach by numerically computing the ground-state properties of the ferromagnetic spin-1 transverse-field Ising model on the 2d triangular and 3d stacked triangular lattice, as well as of the hard-core and soft-core Bose-Hubbard models on the triangular lattice. Our results are benchmarked against those obtained with other techniques, such as perturbative continuous unitary transformations and graph projected entangled pair states, showing excellent agreement and also improved performance in several regimes.

### Thermodynamics of the N=42 kagome lattice antiferromagnet and magnon crystallization in the kagome lattice antiferromagnet

Schnack, Jürgen

For the paradigmatic frustrated spin-half Heisenberg antiferromagnet on the kagome lattice we performed large-scale numerical investigations of thermodynamic functions by means of the finite-temperature Lanczos method for system sizes of up to N = 42. We present the dependence of magnetization as well as specific heat on temperature and external field and show in particular that a finite-size scaling of specific heat supports the appearance of a low-temperature shoulder below the major maximum. We also present numerical evidence for the crystallization of magnons below the saturation field at non-zero temperatures for the highly frustrated spin-half kagome Heisenberg antiferromagnet. This phenomenon can be traced back to the existence of independent localized magnons or equivalently flat-band multi-magnon states. We present a loop-gas description of these localized magnons and a phase diagram of this transition, thus providing information for which magnetic fields and temperatures magnon crystallization can be observed experimentally. The emergence of a finite-temperature continuous transition to a magnon-crystal is expected to be generic for spin models in dimension D>1 where flat-band multi-magnon ground states break translational symmetry.

### Non-equilibrium Floquet steady states of time-periodic driven Luttinger liquids

Schneider, Imke

Imke Schneider$^{1,3}$, Serena Fazzini$^1$, Piotr Chudzinski$^2$, Christoph Dauer$^1$, and Sebastian Eggert$^1$ 1) Physics Department and Research Center OPTIMAS, University of Kaiserslautern, 67663 Kaiserslautern, Germany 2) School of Mathematics and Physics, Queens University Belfast, Belfast, UK 3) Institute of Physics, University of Augsburg, 86135 Augsburg, Germany Time-periodic driving facilitates a wealth of novel quantum states and quantum engineering. The interplay of Floquet states and strong interactions is particularly intriguing, which we study using time-periodic fields in a Luttinger liquid with periodically changing interactions. By developing a time-periodic operator algebra, we are able to obtain the complete set of explicit steady state solutions of the time-dependent Schrödinger equation in terms of a Floquet-Bogoliubov ansatz and known analytic functions. Complex valued Floquet eigenenergies occur when integer multiples of the driving frequency approximately match twice the dispersion energy, which correspond to resonant states. Including damping effects we show that this resonant behavior leads to a large number of density excitations. This setup is one or the rare cases, where a complete Floquet solution can be obtained exactly for a time-periodically driven many-body system.

### Identifying non-thermal excitations in experiment

Schuckert, Alexander

Quantum many-body systems are expected to reach local thermal equilibrium during their non-equilibrium dynamics. Recently, however, several systems have been discovered which do not thermalize due to the presence of non-thermal excitations, for example in Rydberg atom chains and confining gauge theories. We show how to identify such excitations directly in experiment without theory input by measuring two-time correlation functions. We present several protocols to measure two-time correlation functions in quantum gas microscopes, trapped ions, superconducting qubits and Rydberg atoms. As examples, we show that in trapped ion chains, confined excitations can be unambiguously identified. Moreover, in the constraint Rydberg atom chain, quantum many-body scars can be identified directly in experiment. Our protocols show how to probe non-thermal excitations in the "quantum advantage" regime inaccessible to numerical methods.

### Nematic quantum criticality in a Dirac semimetal

Schwab, Jonas

We consider Dirac fermions, as realized by a pi-flux tight binding model on a square lattice coupled to an Ising model in a transverse field. The coupling is chosen such that spontaneous ordering of the Ising spins triggers a meandering of the Dirac fermions and thereby a nematic deformation of the Fermi surface. We consider two models where the nematic transition reduces the initial $C_{4V}$ ($C_{2V}$) point-group symmetry to $C_{2V}$ ($2V$). Auxiliary field quantum Monte Carlo simulations reveal continuous transitions in both cases. In contrast to mass generation transitions, nematic terms explicitly break the Lorentz symmetry and do not open a single particle gap. They define new and unexplored quantum phase transitions in semi-metals.

### Microscopic theory of infinite layer nickelates

Schwemmer, Tilman

The observation of superconductivity in strontium-doped NdNiO$_2$ and the following discovery of a superconducting dome in this material and its sister compound: Sr-doped PrNiO$_2$ provide a new avenue to the study of superconductivity in layered oxide materials. We analyze superconducting instabilities of Sr doped NdNiO$_2$ from various vantage points. Starting with first-principles calculations, we adopt a minimal three-orbital model tight binding model, which captures the key low-energy degrees of freedom. We study superconductivity in both models using the random phase approximation. We then approach the problem from a strong coupling perspective, and study the dominant pairing instability in the associated $t$−$J$ model limit. In all instances, the dominant pairing tendency is found in the d$_{x^2−y^2}$ channel, analogous to the cuprate superconductors.

### Magnetostriction in the $J$-$K$-$\Gamma$-$J_3$ model on the honeycomb lattice

Schwenke, Alexander

Using the numerical linked cluster expansion (NLCE) [1], we investigate thermodynamic and magnetoelastic properties of the $J$-$K$-$\Gamma$-$J_3$ spin-$\frac{1}{2}$ model on the honeycomb lattice in the presence of a magnetic field $B$. Apart from the specific heat and the magnetic susceptibility, we focus in particular on the linear magnetostriction coefficient $\lambda(B,T)$. As a prime result and based on expansions up to order $\sim O(9)$, we find clear indications for a field-induced transition in $\lambda(B,T)$. Employing exchange parameters as proposed for $\alpha\text{-RuCl}_3$, our results are very similar to recently observed experimental data [2] on this proximate quantum spin-liquid candidate material. [1]: M. Rigol et al., Phys. Rev. Lett. 97, 187202 (2006). [2]: S. Gass et al., Phys. Rev. B 101, 245158 (2020).

### Electric, thermal and thermoelectric transport at intermediate temperatures

Schwiete, Georg

Electric, thermal, and thermoelectric transport in correlated electron systems probe different aspects of the many-body dynamics, and thus provide complementary information. These are well studied in the low- and high-temperature limits, while the experimentally important intermediate regime, in which elastic and inelastic scattering are both important, is less understood. To fill this gap, we provide comprehensive solutions of kinetic equations for single band metallic systems and compensated metals in the presence of an electric field and a temperature gradient. We explore the role of the momentum dependence of the impurity scattering rate in the presence of inelastic scattering processes. Specifically, we show that inelastic processes only mildly affect the electric conductivity, but can generate a non-monotonic dependence of the Seebeck coefficient on temperature and even a change of sign. We explore the magnetic field dependence of the Seebeck coefficient and also discuss the Nernst effect. Finally, we address the Lorenz ratio for an impure compensated metal motivated by recent experiments on WP2, which observed a pronounced minimum of the Lorenz ratio at intermediate temperatures.

### Long-Range Hybrid Random Unitary Circuit using Clifford gates

We explore the out-of-equilibrium phases of a special class of system consisting of alternate layers of measurements and unitary matrices, referred to as 'Hybrid Random Quantum Circuits'. In these systems the competition between entangling nature of unitary evolution and disentangling nature of measurements leads to a volume-law to area-law transition in the scaling of entanglement entropy at a fixed non-zero value of rate of measurement. It has been shown that these phase transitions in special analytical limit belongs to the Universality class of specific statistical model's phase transitions. We use 2-site and 2-qubit Clifford unitary gates and projection in Z-direction of the spin as measurements. Starting from a spin chain initially in product state, we explore the effect of range of the unitary circuit in space and in time on the values of the critical point and critical exponents to probe the Universality class of phase transition in the scaling of von-Neumann entnaglement entropy.

### Pentanuclear Spirocyclic Ni4Ln Derivatives: Field Induced Slow Magnetic Relaxation in the Dysprosium and Erbium Analogues

Shukla, Pooja

Five pentanuclear heterometallic isostructural complexes, [Ni4Ln(L)2(LH)2(CH3CN)3Cl]·xH2O·yCH3OH {Ln = YIII (1), GdIII (2), TbIII (3), DyIII (4) and ErIII (5)} [for 1 and 2, x = 2, y = 1; for 3, x = 6, y = 2; for 4, x = 5, y = 1; for 5, x = 2, y = 2] were prepared by the reaction of (E)‐2‐(hydroxymethyl)‐6‐{[(2‐hydroxyphenyl)imino]methyl}‐4‐methylphenol (LH3) with LnCl3·6H2O and Ni(OAc)2·4H2O in the presence of tetrabutylammonium hydroxide (TBA‐OH) base. The structural characterization reveals that compounds 1–5 contain a spirocyclic pentanuclear core [Ni4Ln(µ3‐O)4(µ2‐O)4]3+ where two triangular motifs [Ni2Ln(µ3‐O)2(µ2‐O)2]3+ are fused together through a common vertex of the LnIII ion. The central LnIII ion forms an eight‐coordinated distorted triangular dodecahedron geometry, while the nickel(II) ions form a distorted octahedron geometry. Comprehensive dc magnetic studies reveal that antiferromagnetic exchange interaction exists between the NiII centres. The ac susceptibility measurement revels that dysprosium and erbium analogue shows field induced slow magnetic relaxation with an anisotropic barrier (Ueff) of 25.12 cm–1 and 22.13 cm–1 respectively.

### Fermi polaron dynamics in Open quantum systems

Sighinolfi, Matteo

In ultracold atomic gases a widely studied topic is the impurity problem, where some impurities (e.g. atoms of different species or with different spin) are immersed in a medium of so called majority atoms. When the medium is made of fermionic atoms an impurity forms a quesiparticle called Fermi polaron that results from the dressing of the bare impurities with the excitation of the medium. Static properties of the Fermi polaron are well known and widely studied [1] while the dynamics is less understood. We investigate two different systems of Fermi polaron: the first is a collection of impurities in a fermionic medium, while the second system is composed by a single polaron coupled to a different atomic level via a Rabi frequency. The first system is described with a Keldysh formalism in analogy to what has been done for a quark-gluon plasma in Ref. [2] and the formation of bound state of impurities due to an induced polaron-polaron interaction is discussed. The second system is modelled on the experiment described in Ref [3], where the Rabi coupling is used to investigate the dynamics of the polaron population. Again we use Keldysh formalism, while recently a theoretically study with variational method has been made [4]. With our method we derive quantum Boltzmann equations for the populations in the relevant atomic levels in a similar way to what has been done for quantum Zeno effect in Fermi polarons in dissipative systems [5]. Main properties of the Boltzmann equations and their relation with polaron static properties are shown. Finally, theoretical predictions are compared directly to experimental results where they are also discussed. Bibliography: [1] Massignan, P., Zaccanti, M., & Bruun, G. M. (2014). Polarons, dressed molecules and itinerant ferromagnetism in ultracold Fermi gases. Reports on Progress in Physics, 77(3), 034401. [2] Blaizot, J. P., De Boni, D., Faccioli, P., & Garberoglio, G. (2016). Heavy quark bound states in a quark–gluon plasma: Dissociation and recombination. Nuclear Physics A, 946, 49-88. [3] Scazza, F., Valtolina, G., Massignan, P., Recati, A., Amico, A., Burchianti, A., ... & Roati, G. (2017). Repulsive Fermi polarons in a resonant mixture of ultracold Li 6 atoms. Physical review letters, 118(8), 083602. [4] Adlong, H. S., Liu, W. E., Scazza, F., Zaccanti, M., Oppong, N. D., Fölling, S., ... & Levinsen, J. (2020). Quasiparticle lifetime of the repulsive Fermi polaron. Physical Review Letters, 125(13), 133401. [5] Wasak, T., Schmidt, R., & Piazza, F. (2019). Quantum-Zeno Fermi-Polaron. arXiv preprint arXiv:1912.06618.

### Fulde-Ferrel-Larkin-Ovchinnikov phase and exponential ground state degeneracy in one-dimensional Fermi gas with attractive interactions

Singh Roy, Monalisa

We examine the properties of a one-dimensional (1D) Fermi gas with attractive intrinsic (Hubbard) interactions in the presence of spin-orbit coupling and Zeeman fields. Such a system can be realized in the setting of ultracold atoms confined in a 1D optical lattice, and has been proposed to host exotic topological phases and edge modes. In absence of any external fields, this system shows a trivial Bardeen–Cooper–Schrieffer (BCS) phase. Introduction of Zeeman field takes the system to a Fulde-Ferrel-Larkin-Ovchinnikov phase (FFLO), where the quasi-long range superconducting order co-exists with magnetic order in the system, as indicated by its pair momentum distribution. Next, we explore the effect of spin-orbit coupling in this system. We find that the addition of a smooth parabolic potential yields a phase with exponentially decaying pair binding and excitation energy gaps, which is expected to be associated with topological edge modes in the system. However, we show that this ground state degeneracy is susceptible to local impurities, and argue that the exponential splitting in the clean system is similar to a phase with only conventional order. References: [1] A. E. Feiguin, F. Heidrich-Meisner, G. Orso, and W. Zwerger, Lect. Not. Phys. 836, 503 (2011). [2] Y.-a. Liao, A. Rittner, T. Paprotta, et al., Nature 467, 567 (2010). [3] J. Ruhman, E. Berg, and E. Altman, Phys. Rev. Lett. 114, 100401 (2015). [4] M. Singh Roy, M. Kumar, Jay D. Sau, and S. Tewari, Phys. Rev. B 102, 125135 (2020).

### Incommensurate time crystalline dynamics in an atom-cavity system

Skulte, Jim

Periodically driven atoms in a high finesse optical cavity enjoy a very rich phase diagram. By off resonant driving the equilibrium properties of the system can be renormalised in a controlled fashion, while resonant driving allows for new non- equilibrium phases such as time crystalline phases and dynamical density wave orders as recently reported. In this talk, I will discuss the emergence of an incommensurate time crystal by a phase-modulated transverse pump field, resulting in a shaken lattice. This shaken system exhibits macroscopic oscillations in the number of cavity photons and order parameters at noninteger multiples of the driving period, which signals the appearance of an incommensurate time crystal. The subharmonic oscillatory motion corresponds to dynamical switching between symmetry-broken states, which are nonequilibrium bond ordered density wave states. Employing a semiclassical phase-space representation for the driven-dissipative quantum dynamics, we confirm the rigidity and persistence of the time crystalline phase. We identify experimentally relevant parameter regimes for which the time crystal phase is long lived, and map out the dynamical phase diagram. I will further present preliminary experimental results that confi​rm our theoretical predictions.

### Fragile topological flat bands through adatom superlattice engineering on graphene

Skurativska, Anastasiia

Magic-angle twisted bilayer graphene has received a lot of attention due to its flat bands with potentially non-trivial topology that lead to intricate correlated phases. However, control over the fabrication and thus system parameters of such devices is limited. We propose a single graphene sheet with adatoms periodically placed on top as an alternative system that realizes flat bands.  Performing first principle calculations, we obtain realistic spectra for feasible transition-metal adatoms. Further group-theoretical analysis reveals the fragile nature of topology in some of the flat bands.  We study the bulk-boundary correspondence associated with the fragile topology of the flat bands by building a minimal tight-binding and numerically examine the corner-localized in-gap states, which are a consequence of the filling anomaly resulting from the nontrivial topology. The high control over system parameters makes this system particularly interesting for experimental investigations.

### Weak breaking of translational symmetry in Z2 Topological ordered states

We study Z2 topologically ordered states enriched by translational symmetry by employing a recently developed 2D bosonization approach that implements an exact Z2 charge-flux attachement in the lattice. This allows us to develop a theory of ‘weak symmetry breaking' of translations, which is a remarkable phenomenon beyond traditional symmetry fractionalization. In a weakly symmetry broken state, the ground state remains fully translational invariant, but the symmetry is 'broken' by its anyon quasiparticles. This phenomenon is accompanied by a series of amusing properties such as ground state degeneracy that depends on system size and the emergence of edge gapless Majorana modes. We construct a plethora of exactly solvable models in periodic lattices and also in cylinders and open lattices, that provide an exact illustrations of these anomalies and of the dispersive Majorana gapless boundary modes.

### Quantum magnetism and topological superconductivity in Yu-Shiba-Rusinov chains

Steiner, Jacob

Recent experiments probe subgap excitations in dilute chains of magnetic adatoms on superconducting substrates. In these chains, direct overlap of the adatom d orbitals is negligible, while their Yu-Shiba-Rusinov (YSR) states are still hybridizing. Such YSR chains have also been proposed as a setting for topological superconductivity in the framework of models which assume a frozen texture of classical spins. Motivated by these experiments, we consider quantum spin chains on superconducting substrates and explore their ground state as well as their excitation spectra as relevant for STM experiments. We find that the physics is considerably richer than that of their classical relatives.

### Scattering of mesons in quantum simulators

Surace, Federica Maria

Simulating real-time evolution in theories of fundamental interactions represents one of the central challenges in contemporary theoretical physics. Cold-atom platforms stand as promising candidates to realize quantum simulations of non-perturbative phenomena in gauge theories, such as vacuum decay and hadron collisions. In this talk, I will demonstrate that present-day quantum simulators can imitate linear particle accelerators, giving access to S-matrix measurements of elastic and inelastic meson collisions in low dimensions. Considering for definiteness a $(1+1)$-dimensional $\mathbb{Z}_2$-lattice gauge theory realizable with Rydberg-atom arrays, I will discuss protocols to observe and measure selected meson-meson scattering processes. I will also present a benchmark theoretical study of scattering amplitudes and numerical simulations of realistic wavepacket collisions.

### Many-body localization and quantum many-body systems with artificial gauge fields

Suthar, Kuldeep

The phenomenon of many-body localization (MBL) is attracting significant theoretical and experimental interests over the past few years. The signatures of MBL have been observed in recent cold-atom experiments of optical lattices. The recent experimental advances of artificial gauge fields motivate us to explore the static and dynamical properties of MBL with magnetic flux. We show that the breaking of time-reversal invariance leads to delocalization of spin sector, and the use of spin-dependent uncorrelated disorder potential recovers the complete localization. In the later part, we shall discuss the quantum phase transitions of dipolar bosons and disordered Bose-Hubbard model with synthetic flux, the finite-temperature phase diagrams, the role of anisotropy, and the density-driven staggered superfluidity of dipolar interacting bosons.

### Extended Hubbard model in (un)doped monolayer and bilayer graphene: Selection rules and organizing principle among competing orders

Szabó, András

In this talk I present the effects of generic short-range electronic interactions in monolayer and Bernal bilayer graphene. Typically, at zero doping insulating phases (such as charge-density-wave, antiferromagnet, quantum anomalous and spin Hall insulators) prevail at the lowest temperature, while gapless nematic or smectic liquids stabilize at higher temperatures. On the other hand, at finite doping the lowest temperature ordered phase is occupied by a superconductor. Besides anchoring such an organizing principle among the candidate ordered phases, I also establish a selection rule between them and the interaction channel responsible for the breakdown of the original Fermi liquid. In addition, I demonstrate the role of the normal state band structure in selecting the pattern of symmetry breaking from a soup of preselected incipient competing orders. As a direct consequence of the selection rule, while an antiferromagnetic phase develops in undoped monolayer and bilayer graphene, the linear (biquadratic) band dispersion favors condensation of a spin-singlet nematic (translational symmetry breaking Kekul\'e) superconductor in doped monolayer (bilayer) graphene, when the on site Hubbard repulsion dominates in these systems. On the other hand, nearest-neighbor (next-nearest-neighbor) repulsion accommodates charge-density-wave (quantum spin Hall insulator) and $s+if$ ($s$-wave) pairing at zero and finite chemical doping in both systems, respectively.

### Theory of magnetocaloric effect in V12 molecular magnet: role of quantum level crossings

Szalowski, Karol

Molecular nanomagnets offer a plethora of interesting properties, emerging from the interplay of the geometry and magnetic interactions in small quantum spin clusters. Among them, polyoxovanadates constitute a highly interesting class of cluster nanomagnets. The paper reports a computational study of low-temperature thermodynamic properties of V12 polyoxovanadate molecular magnet, focused on the description of the magnetocaloric effect [1]. The low-temperature magnetic properties of V12 are modeled using an anisotropic quantum Heisenberg Hamiltonian for an ensemble of non-interacting square tetramers. The exchange integrals between the spins S = 1/2 are taken from the experiment [2]. The exact thermodynamic description of the utilized model is constructed using analytic and numerical approach within the canonical ensemble formalism. The quantities of interest are: magnetic entropy and specific heat, isothermal entropy change, refrigerant capacity, adiabatic temperature change as well as magnetic Grüneisen ratio. The energy spectrum of the system of interest exhibits two quantum level crossings between the non-degenerate ground states with different total spin as the external magnetic field is increased. The critical fields for both crossings belong to experimentally accessible range. The importance of quantum level crossing for the low-temperature thermodynamics is demonstrated and emphasized throughout the study. In particular, the residual entropy related to the quantum level crossings is crucial for the magnetocaloric response close to the ground state. For V12 molecular magnet, a robust range of inverse magnetocaloric effect is predicted for cryogenic temperature range and for a significant span of magnetic fields. In particular, the quadratic dependence of the entropy change on the magnetic field amplitude is found for the range of inverse magnetocaloric effect. For the remaining range of temperatures and magnetic fields, a direct magnetocaloric effect occurs. A divergent behaviour of magnetic Grüneisen ratio is predicted at the quantum level crossing points. [1] K. Szałowski, Materials 13, 4399 (2020); doi:10.3390/ma13194399. [2] R. Basler et al., Inorg. Chem. 41, 5675 (2002); doi:10.1021/ic0202099.

### Large scale QMC calculations of the Fermi Velocity renormalization in graphene: bridging the gap between numerics and experiment

Ulybyshev, Maksim

We report on the results of recent Quantum Monte Carlo (QMC) simulations of the effects of electron-electron interactions in graphene. With the help of the Hybrid Monte Carlo algorithm we could achieve unprecedentedly large sample size (up to $102 \times 102$ lattice cells) in fully non-perturbative QMC calculations with strong long-range Coulomb interaction. Thus we could get deeply enough in the infrared regime to directly observe the logarithmic behavior of the Fermi Velocity and to compare its values with both experiment and low-energy effective field theory, which is essentially 2+1D Quantum Electrodynamics. Additional comparison was done with the results of the lattice perturbation theory in one loop and Random Phase approximation. These comparisons allowed us to judge on the numerical accuracy of certain interacting tight-binding Hamiltonian and strongly correlated 2+1D Quantum Electrodynamics in the description of the experimental data for free standing graphene.

### Entanglement entropy scaling transition under competing monitoring protocols

Van Regemortel, Mathias

Dissipation generally leads to the decoherence of a quantum state. In contrast, numerous recent proposals have illustrated that dissipation can also be tailored to stabilize many-body entangled quantum states. While the focus of these works has been primarily on engineering the non-equilibrium steady state, we investigate the build-up of entanglement in the quantum trajectories. Specifically, we analyze the competition between two different dissipation channels arising from two incompatible continuous monitoring protocols. The first protocol locks the phase of neighboring sites upon registering a quantum jump, thereby generating a long-range entanglement through the system, while the second destroys the coherence via a dephasing mechanism. By studying the unraveling of stochastic quantum trajectories associated with the continuous monitoring protocols, we present a transition for the scaling of the averaged trajectory entanglement entropies, from critical scaling to area-law behavior. Our work provides an alternative perspective on the measurement-induced phase transition: the measurement can be viewed as monitoring and registering quantum jumps, offering an intriguing extension of these phase transitions through the long-established realm of quantum optics.

### Quantum dynamics with variational classical networks

Verdel Aranda, Roberto

Dynamics in correlated quantum matter is a hard problem, as its exact solution generally involves a computational effort that grows exponentially with the number of constituents. While remarkable progress has been witnessed in recent years for one-dimensional systems, much less has been achieved for interacting quantum models in higher dimensions, since they incorporate an additional layer of complexity. In this work, we employ a variational method that allows for an efficient and controlled computation of the dynamics of quantum many-body systems in one and higher dimensions. The approach presented here introduces a variational class of wave functions based on complex networks of classical spins akin to artificial neural networks, which can be constructed in a controlled fashion. We illustrate the performance of our method by studying quantum quenches in one- and two-dimensional models. The present work not only supplies a framework to address purely theoretical questions but could also be used to provide a theoretical description of experiments in quantum simulators, which have recently seen an increased effort targeting two-dimensional geometries. Importantly, our method can be applied to any quantum many-body system with a well-defined classical limit. *This work is based on the paper: R. Verdel, M. Schmitt, Y.P. Huang, P. Karpov, M. Heyl, arXiv:2007.16084 (2020).

### Beyond Topological Quantum Chemistry

Vergniory, Maia

Topological quantum chemistry (TQC) framework has provided a complete description of the universal properties of all possible atomic band insulators in all space groups considering  the  crystalline  unitary  symmetries.  It links the chemical and symmetry structure of a given material with its topological properties. While  this  formalism  filled  the  gap  between  the mathematical  classification  and  the  practical  diagnosis  of  topological  materials,  an  obvious  limitation is that it only applies to weakly interacting systems. It is an open question to which extent this formalism can be generalized to   correlated  systems  that  can  exhibit  symmetry  protected  topological  Mott  insulators. In this talk I will first introduce TQC and its application and then I will address this question by combining cluster perturbation theory and topological Hamiltonians within TQC. This simple formalism will be applied to calculate to the phase diagram of a representative model. The results are compared to numerically exact calculations from density matrix renormalization group and variational Monte Carlo simulations together with many-body topological invariants.

### Transport through a dissipative superconducting contact

Visuri, Anne-Maria

In superconducting contacts, the coherent tunneling of a single quasiparticle together with Cooper pairs leads to a sub-gap current structure [1]. This phenomenon, also called multiple Andreev reflections, is well known in condensed-matter superconducting junctions. Current-voltage characteristics consistent with multiple Andreev reflections were also measured in a cold-atom setup where two superfluids are coupled by a quantum point contact [2]. Futher cold-atom experiments have probed transport in the presence of local particle losses [3]. Motivated by such experiments, we investigate theoretically, using the Keldysh formalism, whether a local particle loss at the contact interferes with the multiple Andreev reflection process, and what kind of current-voltage characteristics it leads to. [1] Blonder, Klapwijk, Tinkham, Phys. Rev. B 25, 4515 (1982) [2] Husmann et al., SCience 350, 1498 (2015) [3] Corman et al., Phys. Rev. A 100, 053605 (2019)

### Two-triplon excitations of the Kitaev-Heisenberg-Bilayer

Wagner, Erik

We study the spectrum of a bilayer of Kitaev magnets on the honeycomb lattice coupled by Heisenberg exchange in its quantum-dimer phase for strong interlayer coupling. Using the perturbative Continuous Unitary Transformation (pCUT) we perform series expansion starting from the fully dimerized limit, to evaluate the elementary excitations, reaching up to and focusing on the two-triplon sector. In stark contrast to conventional bilayer quantum magnets, and because of the broken $SU(2)$-invariance, as well as the intralayer directional compass-exchange, the bilayer Kitaev magnet is shown to exhibit a rich structure of two-triplon scattering-state continua, as well as several collective two-triplon (anti)bound states. Direct physical pictures for the occurrence of the latter are provided and the (anti)bound states are studied versus the stacking type, the spin components, and the exchange parameters. In addition to the two-triplon spectrum, we investigate a corresponding experimental probe and evaluate the magnetic Raman-scattering intensity. We find a very strong sensitivity to the two-triplon interactions and the scattering geometry, however a signal from the (anti)bound states only in very close proximity to the continuum.

### Perturbative instability of non-ergodic phases in non-Abelian quantum chains

Ware, Brayden

An important challenge in the field of many-body quantum dynamics is to identify non-ergodic states of matter beyond many-body localization (MBL). Strongly disordered spin chains with non-Abelian symmetry and chains of non-Abelian anyons are natural candidates, as they are incompatible with standard MBL. In such chains, real space renormalization group methods predict a partially localized, non-ergodic regime known as a quantum critical glass (a critical variant of MBL). We argue that such tentative non-ergodic states are perturbatively unstable using an analytic computation of the scaling of off-diagonal matrix elements and accessible level spacing of local perturbations. Our results indicate that strongly disordered chains with non-Abelian symmetry display either spontaneous symmetry breaking or ergodic thermal behavior at long times; we identify the relevant length and time scales for thermalization.

### Fermi-polaron lasing in monolayer charge-tunable semiconductors

Wasak, Tomasz

We study the relaxation dynamics of driven, charge-tuneable monolayer semiconductors in the weak coupling to cavity photons. The itinerant electrons dress the optically pumped excitons to form two Fermi-polaron branches, which are termed as attractive and repulsive polarons. After excitation, a repulsive polaron quickly decays to an attractive polaron at higher momentum via the formation of trions (electron-exciton molecules). The electrons subsequently mediate a slower momentum-relaxation of the attractive polaron, which accumulates population at the edge of the light-cone region around zero momentum where the radiative recombination is the dominant loss channel. Due to the bosonic nature of exciton polarons, around the point where the decay into the attractive polaron overcomes the radiative and non-radiative loss, stimulated processes lead to a transition toward a lasing regime. The latter is characterized by a superlinear increase of light emission as well as extended spatiotemporal coherence. Many-body polaronic effects reduce the emission linewidth below the bare exciton linewidth set by nonradiative loss, as the excitation is partially stored in the electron cloud via the virtual formation of trions.

### Improving topological superconductivity in two- and three-dimensional Josephson junctions

Wastiaux, Aidan

As opposed to the numerous theoretical developments in the field of topological heterostructures hosting robust quasiparticles, difficulties are piling up for experimentalists on their way to building realistic and tunable setups with usable topological states. We address this widespread issue in a specific platform involving a planar Josephson junction made of semiconductor with strong spin-orbit coupling [ref] by proposing easy-to-reach regimes of parameters with enhanced stability of the Majorana end states. Moreover, the extension of those findings to a three-dimensional model provides henceforth a new flexible platform for realizing chiral Majorana edge states. Possible setups using Van der Waals heterostructures are suggested.

### Valence-bond order in two-dimensional antiferromagnets coupled to quantum phonons

Weber, Manuel

The search for valence-bond-solid (VBS) phases in 2D antiferromagnets (AFMs) has attracted a lot of interest due to the proposal of a continuous deconfined quantum phase transition that is beyond the Landau-Ginzburg-Wilson paradigm. While VBS order often appears in frustrated spin systems, large-scale quantum Monte Carlo studies have mainly concentrated on a class of designer Hamiltonians called J-Q models that can be simulated without a sign problem. It is of current interest to find VBS order also in more realistic models. In 1D, a coupling to phonons naturally leads to a dimerization via the spin-Peierls instability, but it is still an open question whether this is also the case in 2D. Here, we use a recently developed quantum Monte Carlo method for retarded interactions to show that a VBS state with Kekule pattern can arise in a spin-Peierls model on the honeycomb lattice. While the AFM—VBS transition is clearly first order for low phonon frequencies, it is tuned towards weakly first-order with increasing quantum lattice fluctuations. Our study reveals that retardation effects have a significant impact on the AFM—VBS transition. Moreover, we discuss our results in relation to frustrated spin models, electron-phonon models, and Dirac systems.

### The Mott Transition as a Topological Phase Transition

Wong, Patrick

We show that the Mott metal-insulator transition in the standard one-band Hubbard model can be understood as a topological phase transition. Our approach is inspired by the observation that the mid-gap pole in the self-energy of a Mott insulator resembles the spectral pole of the localized surface state in a topological insulator. We use numerical renormalization group--dynamical mean-field theory to solve the infinite-dimensional Hubbard model and represent the resulting local self-energy in terms of the boundary Green's function of an auxiliary tight-binding chain without interactions. The auxiliary system is of generalized Su-Schrieffer-Heeger model type; the Mott transition corresponds to a dissociation of domain walls.

### Revisiting the problem of the single hole in an antiferromagnet

Wrzosek, Piotr

Propagation of the single hole introduced into the antiferromagnetic ground state is one of the most studied problems in "cuprate physics", for it can be solved in a relatively controlled manner. Recently a renewed interest into this topic has been triggered by the possibility of simulating hole-doped antiferromagnets in the cold atom experiments [1]. In this contribution I would like to discuss some of our most recent studies on the propagation of the single hole in the antiferromagnet using the magnon language with a special attention paid to the interaction between the magnons [2-3]. To this end, I will introduce an intuitive picture which explains why the electron's spin and charge degrees of freedom can separate in a one-dimensional lattice, though a similar situation cannot occur in two dimensions [2]. Next, I will show that the string potential, which is believed to be felt by the hole moving in a two-dimensional Ising antiferromagnet, is significantly destroyed by the magnon-magnon interactions [3]. [1] C. S. Chiu et al., Science 365, 251 (2019); J. Koepsell et al., Nature 572, 358 (2019). [2] K. Bieniasz et al., SciPost Phys. 7, 066 (2019). [3] P. Wrzosek et al., Phys. Rev. B 103, 035113 (2021).

### Exceptional Spin Liquids

Yang, Kang

We establish the appearance of a qualitatively new type of spin liquid with emergent exceptional band-touching behaviours when coupling to the environment. We consider an open system of the Kitaev model generically coupled to an external environment. In extended parameter regimes, the usual band crossings of the emergent Majorana fermions from the original model are split into exceptional band crossings. In glaring contrast to the original gapless phase of the honeycomb model which requires time-reversal symmetry, this new phase is stable against all perturbations. The system also displays a large sensitivity to boundary conditions resulting from the non-Hermitian skin effect with telltale experimental consequences. Our results point to the emergence of new classes of spin liquids in open systems which might be generically realized due to unavoidable couplings with the environment.

### Hall effect in Sr2RuO4 under <100> uniaxial pressure

Yang, Po-Ya

The Hall coefficient of Sr2RuO4 goes through two sign changes, at $\sim$120 K and 30 K. It has been proposed that this temperature dependence is due to strong orbital differentiation of the inelastic scattering rates, which is a predicted consequence of strong Hund’s coupling. Here, in order to probe this hypothesis, we report the Hall resistance of Sr2RuO4 under tunable uniaxial stress. The gamma Fermi surface sheet of Sr2RuO4 is driven through a Lifshitz transition by uniaxial pressure along a <100> direction. At a temperature where resistivity is dominated by electron-electron scattering, the Hall coefficient becomes less electron-like while approaching the van Hove singularity, which supports the Hund’s coupling scenario in the three-band system. At very low temperature, however, despite the change in topology of the Fermi surface structure both the Hall resistivity and longitudinal resistivity are essentially unchanged across the Lifshitz transition, which is not expected in any simple model of transport in Sr2RuO4.

### One-dimensional ultracold bosons in shallow quasiperiodic systems: Bose glass phase and fractal Mott lobes

Yao, Hepeng

The emergence of a compressible insulator phase, known as the Bose glass, is characteristic of the interplay of interactions and disorder in correlated Bose fluids. While widely studied in tight-binding models, its observation remains elusive owing to stringent temperature effects. In this talk, I will present our results about the study of ultracold bosons in shallow 1D quasiperiodic potentials. First, I will start with the non-interacting case. Thanks to the exact diagonalization techniques, we determine the critical properties and the Hausdorff fractal dimension of the system [1]. Then, we move to the study of the interacting case based on the results of the ideal bosons. With the quantum Monte Carlo calculations, we compute the phase diagram of Lieb-Liniger bosons in shallow quasiperiodic potentials [2]. A Bose glass, surrounded by superfluid and Mott phases, is found. At finite temperature, we show that the melting of the Mott lobes is characteristic of a fractal structure and find that the Bose glass is robust against thermal fluctuations up to temperatures accessible in experiments. [1] H. Yao, H. Khoudli, L. Bresque, L. Sanchez-Palencia. Phys. Rev. Lett. 123, 070405 (2019). [2] H. Yao, T. Giamarchi, L. Sanchez-Palencia,Phys. Rev. Lett. 125(6), 060401 (2020).

### Residual bulk viscosity of a disordered 2D electron gas

The nonzero bulk viscosity signals breaking of the scale invariance. We demonstrate that a disorder in two-dimensional noninteracting electron gas in a perpendicular magnetic field results in the nonzero disorder-averaged bulk viscosity. We derive analytic expression for the bulk viscosity within the self-consistent Born approximation. This residual bulk viscosity provides the lower bound for the bulk viscosity of 2D interacting electrons at low enough temperatures. https://arxiv.org/abs/2102.10533

### Orthogonal quantum many-body scars

Zhao, Hongzheng

Quantum many-body scars have been put forward as counterexamples to the Eigenstate Thermalization Hypothesis. These atypical states are observed in a range of correlated models as long-lived oscillations of local observables in quench experiments starting from selected initial states. The long-time memory is a manifestation of quantum non-ergodicity generally linked to a sub-extensive generation of entanglement entropy, the latter of which is widely used as a diagnostic for identifying quantum many-body scars numerically as low entanglement outliers. Here we show that, by adding kinetic constraints to a fractionalized orthogonal metal, we can construct a minimal model with orthogonal quantum many-body scars leading to persistent oscillations with infinite lifetime coexisting with rapid volume-law entanglement generation. Our example provides new insights into the link between quantum ergodicity and many-body entanglement while opening new avenues for exotic non-equilibrium dynamics in strongly correlated multi-component quantum systems.

### Subdiffusive dynamics and critical quantum correlations in a disorder-free localized Kitaev honeycomb model out of equilibrium

Zhu, Guo-Yi

Disorder-free localization has recently emerged as a mechanism for ergodicity breaking in homogeneous lattice gauge theories. In this work we show that this mechanism can lead to unconventional states of quantum matter as the absence of thermalization lifts constraints imposed by equilibrium statistical physics. We study a Kitaev honeycomb model in a skew magnetic field subject to a quantum quench from a fully polarized initial product state and observe nonergodic dynamics as a consequence of disorder-free localization. We find that the system exhibits a subballistic power-law entanglement growth and quantum correlation spreading, which is otherwise typically associated with thermalizing systems. In the asymptotic steady state the Kitaev model develops volume-law entanglement and power-law decaying dimer quantum correlations even at a finite energy density. Our work sheds light onto the potential for disorder-free localized lattice gauge theories to realize quantum states in two dimensions with properties beyond what is possible in an equilibrium context.