Korrelationstage 2025

We theoretically investigate the thermoelectric phenomena in an altermagnet-based superconducting junction. The novel characteristic of the newly discovered magnetic material, known as altermagnet, carries the property of non-relativistic spin-splitting of the energy bands with zero net magnetization. We study the effect of this finite energy spin splitting to the thermoelectric properties of the superconductor-altermagnet heterojunction by computing the thermoelectric particle current. We also study the particle current due to the superconducting phase difference in the Josephson junction. Utilizing the spin-split nature of this novel magnetism, we also establish the thermoelectric Josephson diode effect in our alternagnetic Josephson junction.

We demonstrate that the chiral $\mathbb{Z}_p$ toric code model -- a quintessential example of topological order --- hosts additional, emergent topological phases when perturbed: descendant fractional quantum Hall states, which we term \textit{Hall-on-Toric}. The additional topological order induces an enhanced topological ground-state degeneracy. The states are formed by defects of the star operators, which experience an effective magnetic flux caused by the plaquette terms. We confirm their existence through extensive infinite density matrix renormalization group (iDMRG) simulations, analyzing the topological entanglement entropy, entanglement spectra, and a generalized Hall conductance. Remarkably, these descendant states remain robust even in the absence of $U(1)$ symmetry. Our findings reinforce the foundational interpretation of star and plaquette defects as magnetic and electric excitations, and reveal that this perspective extends to a much deeper level.

We study the effect Markovian dephasing has in the single impurity Anderson model. The quantum dot is attached to two metallic leads. In equilibrium, we investigate the spectral and distribution function and discuss the role of dephasing on Kondo physics. In the steady state, out of equilibrium, we compute the conductance as a function of applied voltage and find a universal scaling behavior, with a dephasing dependent Kondo scale.

For quantum spin systems in equilibrium, the dynamic structure factor (DSF) is among the most feature-packed experimental observables. However, from a theory perspective it is often hard to simulate in an unbiased and accurate way, especially for frustrated and high-dimensional models at intermediate temperature. We address this challenge by introducing a dynamic extension of the high-temperature expansion as an efficient numerical approach to the DSF for arbitrary lattices. We focus on the nearest-neighbor Heisenberg model and spin-lengths S=1/2 and 1. We present a user-friendly numerical implementation and provide comprehensive benchmarks on spin chains. As applications we treat a variety of frustrated two- and three dimensional antiferromagnets. In particular we shed new light on the anomalous intermediate temperature regime of the S=1/2 triangular lattice model and reproduce the DSF measured recently for a S=1 pyrochlore material.

Effective low-energy descriptions of strongly correlated condensed matter systems — such as 2D Dirac semi-metals — can be written as Gross-Neveu-Yukawa-type theories. These relativistic quantum field theories capture the universal behaviour near quantum critical points, and capture spontaneous symmetry-breaking throughout large parameter ranges such as temperature and even small deviations from half filling. The description in terms of relativistic fermions suggests the analogy to mechanisms in Quantum Chromodynamics (QCD), where strongly correlated fermions create a rich phase diagram at low energies. Functional Renormalization Group (fRG) methods provide a non-perturbative tool capable of accessing regimes which are obstructed by the sign-problem in quantum Monte Carlo simulations and are being actively developed to also detect e.g. color-superconducting or inhomogeneous phases. In my talk I want to discuss numerical tools developed for the fRG in a QCD context, specifically focusing on the quantitative resolution of first and second order phase transitions. I also want to highlight the versatility of generalised fRG techniques which were recently shown to quantitatively capture instanton-mediated tunnelling.

I will introduce the quantum geometry effect in superconductivity and delocalization. In flat-band systems, the Fermi velocity vanishes and the effective mass diverges, leading to the failure of conventional BCS relations, such as the coherence length ξ=ℏv_f/Δ and the superfluid weight D_s∝ 1/m^*. I will discuss the establishment of Ginzburg-Landau (GL) theory concerning the coherence length of flat-band superconductors. From this theory, we find that the superconducting coherence length is not determined by Fermi velocity but rather by the size of optimally localized Wannier functions, which is constrained by the quantum metric. Furthermore, I will explore the interplay between quantum geometry, interactions, and external fields in complex band systems. When Wannier obstructions prevent a description based solely on atomic-like orbitals, it complicates the prediction of electromagnetic responses, particularly in the presence of disorder and interactions. To address this, we introduce a generalized Peierls substitution framework that incorporates Lagrange multipliers to enforce the constraints of Wannier obstruction in the band of interest. This framework enables us to derive effective descriptions of interactions and disorder, accounting for the non-trivial quantum geometry of the band. We apply this approach to various examples, including the diamagnetic response in flat-band superconductors and interaction-induced delocalization effects in flat-band metals.

The quest for novel states of matter is important both on fundamental grounds and in view of possible applications, with superconductivity and the various quantum Hall effects being outstanding examples. This talk will summarize recent developments in the field, with an emphasis on the effects on frustration and intrinsic topological order. I will highlight frustration-based routes to novel forms of order and disorder, non-Fermi liquid metals and exotic superconductivity, and I will discuss aspects on quantum phase transitions between the various phases. Connections to experiments on kagome and pyrochlore metals as well as cuprate high-temperature superconductors will be made.

The search for Majorana particles is crucial both for fundamental physics and potential topological quantum computation. Since Majoranas are an equal superposition of particle and antiparticle, they are naturally sought in superconductors as Majorana zero modes (MZMs). The search for new compounds hosting robust MZMs requires a deeper understanding of these states. Fu and Kane [1] showed that a MZM can emerge in the vortex-core states of an s-wave superconductor on top of a strong topological insulator (TI). It would be then natural to propose that high-temperature cuprates would enhance the MZMs protection, as it was done in [2]. However, when considering vortices inside a d+id-wave superconductor on top of a TI, the stability of MZMs is limited by additional in-gap states within vortices. Moreover, our numerical simulations reveal an asymmetry in the appearance of MZMs between vortices and antivortices. When combined, MZMs can vanish. In this context, we discuss the stability of Majorana zero modes arising from vortex core states in topological superconductors. [1] Liang Fu, and C. L. Kane, Phys. Rev. Lett. 100, 096407 (2008). [2] A. Mercado, S. Sahoo, and M. Franz, Phys. Rev. Lett. 128, 137002 (2022) [3] G. Venditti, C. Berthod, L. Rademaker, In preparation (2025)

The enigmatic heavy-fermion compound UTe2 is a strong candidate for bulk odd-parity spin-triplet superconductivity. While its low, orthorhombic crystal symmetry favors a single-component bulk superconducting order parameter, some experimental observations challenge this expectation. Notably, conflicting reports of time-reversal symmetry (TRS) breaking at the critical temperature, primarily detected by surface-sensitive probes, raise the possibility of TRS breaking originating from surface phenomena. Adding to this complexity, a charge-density wave (CDW) order has been observed on the easy-cleave surface, exhibiting a curious interplay with superconductivity and a nontrivial evolution of its Fourier peaks under an applied magnetic field. We demonstrate that the CDW transforms under a two-component representation of the surface symmetry group and analyze its coupling to a magnetic field. Furthermore, we explore the intertwining of bulk homogeneous superconductivity with the surface CDW, which induces a two-component pair-density wave on the surface. We show that this induced pairing opens the possibility of surface TRS breaking. Our analysis therefore sheds light on the interplay between bulk and surface physics in UTe2. [1] A. S., A. Ramires, arXiv:2503.24390

Nonsymmorphic symmetries have been on the spotlight in condensed matter physics since the advent of topological band theory and, most recently, have been highlighted in the context of altermagentism. In this talk, I will briefly introduce nonsymmorphic symmetries and discuss two other scenarios in which the presence of nonsymmorphic symmetries can lead to novel physical phenomena. The first example concerns superconductivity-induced odd-parity orders inspired by the phenomenology of the heavy-fermion CeRh2As2. The second example involves the protection of a ferromagnetic quantum critical point against its transmutation to a first order phase transition. A. Szabo and A. Ramires, Physical Review B 110 (18), L180503 (2024) S. Shin, A. Ramires et al., Nature Communications 15 (1), 8423 (2024)

Solving the many-electron problem, even approximately, is one of the most challenging and simultaneously most important problems in contemporary condensed matter physics with various connections to other fields. The standard approach is to follow a divide and conquer strategy that combines various numerical and analytical techniques. A crucial step in this strategy is the derivation of an effective model for a subset of degrees of freedom by a procedure called downfolding, which often corresponds to integrating out energy scales far away from the Fermi level. In this work we present a rigorous formulation of this downfolding procedure, which complements the renormalization group picture put forward by Honerkamp [PRB 85, 195129 (2012)]. We derive an exact effective model in an arbitrarily chosen target space (e.g. low- energy degrees of freedom) by explicitly integrating out the the rest space (e.g. high-energy degrees of freedom). Within this formalism we state conditions that justify a perturbative truncation of the downfolded effective interactions to just a few low-order terms. Furthermore, we utilize the exact formalism to formally derive the widely used constrained random phase approximation (cRPA), uncovering underlying approximations and highlighting relevant corrections in the process. Lastly, we detail different contributions in the material examples of fcc Nickel and the infinite-layer cuprate SrCuO2. Our results open up a new pathway to obtain effective models in a controlled fashion and to judge whether a chosen target space is suitable. [1] [1] arXiv:2507.16916

We present a microscopic pairing mechanism in which the kinetic energy of pairs is much lower than the kinetic energy of electrons. This results in interaction-driven localization of charge without extrinsic disorder and is characterized by a vanishing superfluid stiffness. Localized pairs gain more kinetic energy from resonating between sublattices in a bosonic compact localized state, than from delocalizing throughout the material. This is grounded in a microscopic model building on a structural motif shared by many oxide superconductors strongly interacting localized electrons realize spin degrees of freedom on the vertices and doped charge lives on the edges of the Bravais lattice. In the strong-coupling limit, local unconventional pairs realize the bosonic analog of flat bands supported on line graphs. We discuss the experimental implications of this pairing mechanism, with concrete falsifiability criteria, and emphasize the broad scope of this recipe in connection to diverse families of strongly correlated materials which share the key ingredients that go into it.

We investigate the transport properties of one-dimensional systems beyond linear response, focusing on the fractionalization of propagating charges. Starting from a right-moving unit charge, we predict its evolution into at least three distinct stable parts: a fractionally charged particle with free- particle dynamics, a left-moving signal, and a right-moving low-energy excitation, which can carry positive or negative charge depending on the interaction strength and energy regime. Our findings provide deep insights into the universal correlated nature of these emergent particles and pave the way for out-of-equilibrium transport measurements, offering a direct method to extract the interaction parameters governing correlations in the system.

Electron-phonon interactions are fundamental to quantum materials and lead to a variety of correlated phenomena like the formation of polarons, superconductivity, or charge order. However, their numerical simulation is often hindered by the unbound bosonic Hilbert space of the phonons and long autocorrelation times. The directed-loop quantum Monte Carlo method for retarded interactions overcomes these issues in one dimension and enables us to solve these systems with unprecedented precision [1]. In this talk, I reconsider the one-dimensional Hubbard-Holstein model which, for many years, was believed to only host an intermediate metallic phase between spin- and charge-density-wave states which has been debated to be a Luther-Emery liquid. Here I report the discovery of a novel intermediate phase at strong couplings which exhibits bond order [2]. The latter does not result from a Peierls instability but is reminiscent of the intermediate phase in the extended Hubbard model. However, in our case it is driven by competing frequency dependencies of a dynamically screened Hubbard interaction. We find a continuous quantum phase transition between charge and bond orders separated by a deconfined critical point that only turns first order at strong couplings. I show that the same transition can be found from competing electron-phonon interactions as a result of quantum lattice fluctuations. All in all, electron-phonon interactions can lead to phase diagrams and critical phenomena that are significantly more complex than always thought, motivating future studies also in higher dimensions. [1] M. Weber, F. F. Assaad, M. Hohenadler, Phys. Rev. Lett. 119, 097401 (2017) [2] M. Weber, arXiv:2412.13263

The $J_1$-$J_2$ spin chain is one of the canonical models of quantum magnetism, and has long been known to host a critical antiferromagnetic phase with power-law decay of spin correlations. Using the matrix product state path integral to capture the effects of entanglement near the saddle points, we argue here that there are, in fact, two distinct critical phases: the ‘Affleck-Haldane’ phase, where the dimer field that parametrises local singlet order is part of a joint O(4) N\’eel-singlet order parameter; and the ‘Zirnbauer’ phase, where the dimer field is gapped out and the critical theory involves only an O(3) N\’eel order parameter. We describe a similar critical-to-critical transition in a model of three coupled spin chains. The phases are so-named because each realises one of the competing pictures for how the O(3) non-linear sigma model with a topological theta term renormalises to the \mathfrak{su}(2)_1 Wess-Zumino-Witten model.

Recent advances in quantum technology allow the realization of "lattice anyons", which have enjoyed large interest as particles which interpolate between bosonic and fermionic behavior. We now study the interplay of such fractional statistics with strong correlations in the one-dimensional extended Anyon Hubbard model at unit filling by developing a tailored bosonization theory and employing large-scale numerical simulations. The resulting phase diagram shows several distinct phases, which show an interesting transition through a multicritical point. As the anyonic exchange phase is tuned from bosons to fermions, an intermediate coupling phase changes from Haldane insulator to a dimerized phase. Detailed results on the universality of the phase transitions are presented.

I will present recent advances in the study of correlated Mott systems driven into nonequilibrium steady states. The analysis is based on an impurity solver that combines Keldysh Green’s functions with the Lindblad formalism for open quantum systems [1], embedded within nonequilibrium Dynamical Mean-Field Theory. Recent methodological improvements including a Configuration Interaction treatment of the many body Lindblad equation combined with a linear functional interpolation [2] allow to address scaling behavior in the Kondo regime. I will discuss nonequilibrium phenomena such as photovoltaic effects and multiple-carrier generation via impact ionization in photoexcited Mott insulators [3]. Finally, I will outline perspectives for addressing multiorbital systems and realistic material simulations out of equilibrium [4]. [1] E. Arrigoni et al., Phys. Rev. Lett. 110, 086403 (2013); A. Dorda et al., Phys. Rev. B 89 165105 (2014); A. Dorda et al., Phys. Rev. B 92, 125145 (2015) [2] D. Werner et al., Phys. Rev. B 107, 075119 (2023); D. Werner and E. Arrigoni, PRR Letters 7, 6 (2025) [3] M. Sorantin et al., Phys. Rev. B 97, 115113 (2018); P. Gazzaneo et al. Phys. Rev. B 106, 195140 (2022); Phys. Rev. B 109, 235134 (2024); New J. Phys. 27, 033008 (2025) [4] T. M. Mazzocchi et al. arXiv:2507.10717 (2025)

Mott insulators with strong spin-orbit coupling and localized moments are increasingly being recognized as platforms for emergent multipolar phenomena. This study expands the conventional concept of multiferroicity—where ferroelectric and ferromagnetic orders coexist—to encompass higher-order multipolar degrees of freedom, specifically in 4d and 5d Mott insulators characterized by strong spin-orbit and Hund's couplings. Our findings reveal that a combination of quadrupolar and octupolar magnetic orders can simultaneously induce both electrical quadrupolar moments and ferroelectric polarization, demonstrating the potential for coexisting multipolar orders of varying or the same ranks. Furthermore, we report a surprising response of a 4d or 5d Mott insulator to circularly polarized light, which induces an emergent static “magnetization” that specifically couples to the material's magnetic octupole moments, leaving the quadrupolar moments unaffected. This selective coupling, driven by a light-induced flux within transition metal-ligand-transition metal clusters, effectively manifests as an octupolar Zeeman effect. It presents a novel mechanism for light-induced symmetry breaking and macroscopic polarization. Notably, the induced magnetization results in significant lattice deformations, which could be measured by X-ray diffraction as a hallmark signature of the underlying hidden order. Refs. 1) S. Banerjee, S. Humeniuk, A. R. Bishop, A. Saxena, and A. V. Balatsky, Multipolar multiferroics in 4⁢????2/5⁢????2 Mott insulators Phys. Rev. B 111, L201107 (2025) 2) S. Banerjee, A. Tyner, G. W. Fernando, M. Eschrig, and A. V. Balatsky, Detecting light-induced octupolar order in Mott insulators, [under preparation]

Spin-dependent band splitting is one of the characteristic features of altermagnets, but a conventional band picture may not be applicable in the case of Mott altermagnets. We employ two numerical methods, the self-consistent Born approximation and the variational cluster approach, to study hole motion in Mott altermagnets. Our results reveal that spin-dependent spectral-weight transfer is the dominant signature of Mott altermagnetism. This pronounced spin–momentum locking of the quasiparticle spectral weight arises from the formation of altermagnetic polarons, whose dynamics are governed by the interplay between free hole motion and the coupling of the hole to magnon excitations in the altermagnet. We demonstrate this effect by calculating ARPES spectra for two canonical altermagnetic systems: the checkerboard $J_1$–$J_2$ model and the Kugel–Khomskii spin–orbital altermagnet in a model based on vanadates.

External drives, such as for example irradiation with a laser, can push a system out of thermal equilibrium. Here, we show how drives that manifest as effective single body pumps can induce transitions into manifestly nonthermal phases of matter. These are characterised by a dynamical order parameter that traces out a limit cycle in the stable state, thereby breaking time translation symmetry. We employ dynamic RG techniques to determine the universal phenomena at the ensuing transitions in $d$-dimensional $O(N)$ models: The transition between a symmetric and a limit cycle phase defines a new, genuinely nonthermal universality class without an equilibrium counter part. The transition from an ordered into the limit-cycle phase occurs through a critical exceptional point which we show cause a fluctuation-induced first order transition. We show, that the Goldstone-modes within the dynamical phases are a realisation of the KPZ universality class and offer new generalisations of KPZ to larger symmetry groups. We complement these findings by showing that these phenomena can for instance be induced through rapid parametric drives of equilibrium systems coupled to a cold bath as well as weakly irradiating a ferrimagnetic spin system. Furthermore, we connect our results to recent advances in nonreciprocal active matter.

Rydberg simulators, superconducting qubit arrays and other quantum simulation platforms are increasingly able to simulate isolated quantum many-body dynamics in two spatial dimensions, and explore uncharted territory for theory. For example, recent experiments study order parameter dynamics in both slow ramps and (fast) quenches involving phase transitions, thereby placing the physics of quantum coarsening in the experimental realm. Here, we present a theory for this non-equilibrium dynamics.

The properties of interfaces are key to understand the physics of matter. However, the study of quantum interface dynamics has remained an outstanding challenge. We use large-scale Tree Tensor Network simulations to identify the dynamical signature of an interface roughening transition within the ferromagnetic phase of the 2D quantum Ising model. For initial domain wall profiles we find extended prethermal plateaus for smooth interfaces, whereas above the roughening transition the domain wall decays quickly. Our results can be readily explored experimentally in Rydberg atomic systems.

Since the beginning of intensive research on copper oxides in the late 1980s, it has been recognized that ligands play an important role in their correlated physics. Most early studies focused on identifying the minimal model needed to explain superconductivity -- specifically, whether ligands are essential in this context. In this contribution, however, I discuss two recent works that highlight the crucial role of ligands in revealing other (novel) phenomena in the cuprates. First, I show that the recent observation of orbital waves (orbitons) in two layered cuprates can only be explained by models incorporating strong correlations on oxygen sites [1]. Second, I argue how ligands may enable the emergence of altermagnetism in these materials [2]. [1] L. Martinelli et al., "Collective nature of orbital excitations in layered cuprates in the absence of apical oxygens"; Phys. Rev. Lett. 132, 066004 (2024). [2] Y. Li et al., "d-Wave Magnetism in Cuprates from Oxygen Moments"; arxiv:2412.11922.

Exact functional renormalization group (FRG) flow equations for quantum systems can be derived directly within an operator formalism without using functional integrals. This simple insight allows us to apply unbiased FRG methods directly to strongly correlated electron systems with projected Hilbert spaces. Here, we use this approach to compute the phase diagram and spectral function of the Hubbard model at infinite on-site repulsion and finite temperatures. Besides the Fermi liquid at low density, we also obtain the Nagaoka ferromagnet at high density and an intermediate stripe phase. We observe striking indications of non-Fermi-liquid physics, including pseudogaps, the emergence of Luttinger surfaces and Fermi arcs, and the breakdown of the Luttinger theorem.

We present an approach to systematically search for ground states for quantum lattice models with algebraically decaying long-range interactions in the thermodynamic limit without truncating the interaction. The approach is based on the observation that the classical energy of a long-range interaction of a periodic state can be evaluated in the thermodynamic limit on the unit cell of the state using appropriately resumed couplings. By optimizing appropriate resumed energy functions on relevant unit cells and comparing the energies in the thermodynamic limit between them one obtains estimates for the ground state in the thermodynamic limit only limited by the size of the considered unit cells and the optimization algorithm used. This approach naturally enables mean-field calculations for quantum spin models with long-range interactions without truncation of the interactions and provides a path to study frustrated spin models in the thermodynamic limit without bias from the considered geometries. We present results for relevant boson lattice models for cold Erbium atom quantum simulation platforms. Further, we also show recent results for the paradigmatic Dicke-Ising model of light-matter interactions with algebraically decaying long-range couplings. In both examples the long-range interactions change the ground state phase diagrams drastically, introducing a devil’s staircase of crystalline phases and stabilizing exotic non-trivial phases.

Effective band structures, or momentum space patches are frequently used to address the dominant low energy physics. These effective models inherently result in long range matrix elements which seemingly contradict the mantra of locality in physics. Here, we perform large scale quantum Monte Carlo simulations of a Hamiltonian formulation of Dirac fermions (SLAC fermions) competing with a local Coulomb interaction which allow to investigate the quantum phase transition from Dirac semi-metal to antiferromagnetic insulator at unprecedented accuracy. We directly compare this approach against established large scale simulations of electrons on the hexagonal lattice. We find clear evidence for the explicit reduction of finite size effects attributed to the optimised free Dirac dispersion of the SLAC fermions. The critical properties agree on both implementations for very large system sizes, where the SLAC formulation clearly outperforms the honeycomb. We affirm the reliability of our approach by thorough tests for non-physical artefacts of the non-local Hamiltonian and its dynamically induced long-range interactions in the phases and at criticality. We further investigate the major-axis coupled, long-range quantum Heisenberg model in two spatial dimensions at finite and zero temperature as representative worst case scenario. We quantify the effects of sub-volume anisotropic long range spin-coupling with power-law form ${1/r^{\alpha}}$ on the critical exponents of the transitions where SU(2) spin symmetry is spontaneously broken for at low, finite temperatures in accordance with the Mermin Wagner Hohenberg theorem. For different $\alpha$ we determine the extent of the regimes where the (quantum) phase transitions are represented by Gaussian fixed point, short-range Wilson-Fisher, or continuously varying long-range non-Gaussian critical exponents.

Superconductivity has been observed in twisted MoTe$_2$ within the anomalous Hall metal parent state~\cite{Xu2025SC}. Key signatures—including a fully spin/valley polarized normal state, anomalous Hall resistivity hysteresis, superconducting phase adjacent to the fractional Chern insulating state and a narrow superconducting dome at zero gating field—collectively indicate chiral superconductivity driven by intravalley pairing of electrons. Within the Kohn-Luttinger mechanism, we compute the superconducting phase diagram via random phase approximation, incorporating Coulomb repulsion in a realistic continuum model. Our results identify a dominant intravalley pairing with a narrow superconducting dome of $p+ip$ type at zero gating field. This chiral phase contrasts sharply with the much weaker time-reversal-symmetric intervalley pairing at finite gating field. Our work highlights the role of band topology in achieving topological superconductivity, and reveals the chiral and topological nature of the superconductivity observed in twisted MoTe$_2$.

We study the phase diagram of twisted bilayer graphene at charge neutrality as a function of twist angle $\theta$ and temperature $T$ using sign-problem-free quantum Monte Carlo simulations. At $T=0$, we find a continuous transition from a Dirac semimetal to a gapped Kramers inter-valley coherent (KIVC) phase as $\theta$ decreases toward the magic angle. In the KIVC phase, the entropy rises sharply with temperature and plateaus at $15,\text{K} \lesssim T \lesssim 60,\text{K}$ near the value expected from a Mott-like regime of localized electrons with nearly uncorrelated spin, valley, and orbital degrees of freedom. The spectral function evolves continuously with $\theta$: at low $T$, a gap opens at the $K$ points and shifts toward $\Gamma$ as $\theta$ decreases; at intermediate $T$, it smoothly interpolates between a Dirac semimetal with coherent $K$-point quasiparticles and a state with gapless $\Gamma$-centered quasiparticles near the magic angle.

In this talk, I will present theoretical results on quantum phase transitions in moiré materials tuned by twist angle and pressure. In twisted bilayer graphene, we uncover a continuous transition from a Dirac semimetal to a Kramers intervalley-coherent insulator, which belongs to the Gross-Neveu-XY universality class. In twisted double bilayer transition metal dichalcogenides, we identify a continuous transition from a Dirac semimetal to an antiferromagnetic insulator with spin-density modulation at the moiré scale. This transition realizes the Gross-Neveu-Heisenberg universality class. These findings provide theoretical context for, and help clarify, recent experimental observations of such a transition in twisted double bilayer WSe2.

Fractional topological insulators (FTIs) are time-reversal symmetric states exhibiting topological order, including fractionalized excitations and topological ground state degeneracy. Moiré systems such as twisted MoTe2 have recently emerged as a potential platform for experimentally realizing such states. Twisted MoTe2 at 3.7 degrees hosts a pair of time-reversal related flat Chern bands and may therefore host FTIs at fractional filling of those bands. In this theoretical work, we study the criteria for stabilizing an FTI. In particular, we perform exact diagonalization on a Landau level model to establish the conditions that the interaction should satisfy for such a phase to be realized. Next, we apply this knowledge to a realistic model of twisted MoTe2 and establish the phase diagram at filling factor 2/3, where an Abelian FTI is shown to be realized. We discuss how to stabilize the phase using dielectric engineering.

Time-periodic driving has become a valuable tool in Floquet engineering of many-body systems in the high frequency limit, but the understanding and utilization of resonances in many-body systems at lower frequencies still remains difficult. After a short discussion of the treatment of resonances with Floquet theory [4], an alternative mechanism of tuning resonant interactions between cold atoms is proposed, which is based on dynamically creating "Floquet bound states" using time-periodic fields [1]. The resulting predictions explain recent experimental data and provide additional tuning possibilities. By adjusting amplitude, frequency and mean of the applied oscillating field it is possible to accurately choose location and width of clean scattering resonances over a wide range. This paves the road to a versatile toolbox of tailored interactions in setups with multiple species.

We explore the robustness of Hall conductivity quantization under various Hamiltonians, exhibiting one scenario where the quantization is not preserved. Specifically, we apply the Kubo formula to topological models with the Hatsugai-Kohmoto interaction. Starting from the many-body degeneracy induced by this interaction in the topological Kane-Mele model, we consider Zeeman fields to select specific states within the ground-state manifold that reveal a non-quantized Hall response. We present a system that breaks this quantization through a Hamiltonian incorporating a Zeeman field diagonal in the bands of the Kane-Mele model. From a physical point of view, this term may mimic a ferromagnetic order that arises naturally when couplings beyond the Hatsugai Kohmoto interaction are taken into account.

We present an analysis of the orbital Hall effect in confined geometries, with an emphasis on the effects of non-Ohmic flows and unconventional relaxational properties. A key result is that the effective orbital angular momentum decay rate follows a Dykonov-Perel-scaling and is inversely proportional to the electron scattering rate, even if the latter is small. We show that non-Ohmic flows and spatially varying electric fields result in contributions to the OHE which are distinct from the well known intrinsic and extrinsic mechanisms, including non-local and vorticity induced accumulations of orbital angular momentum.

Motivated by recent discovery of additional topologically non-trivial phases of matter in lattice models beyond established classification schemes, we generalise the framework of the quantum Hall effect (QHE) to that of the quantum skyrmion Hall effect (QSkHE). This involves one key generalisation: considering particles on a two-sphere, which see a U(1) monopole, one can project to the lowest Landau level (LLL). Upon performing such a projection, the position coordinates become proportional to SU(2) generators by quenching of kinetic energy. An almost point-like LLL corresponds to matrix representation size for the SU(2) generators of N by N, with N small. The key generalisation is that such an almost point-like LLL with small orbital degeneracy can still host an intrinsically 2+1 dimensional topologically non-trivial many-body state. Equivalently, in regimes in which spin has previously been treated as a label (small N), spin encodes some finite number of spatial dimensions, in general. This many-body state can play the role, in the QSkHE, that a charged particle plays in the QHE.