Quantum Materials in the Quantum Information Era

Long coherence times can be achieved in randomly doped systems by targeting collective few-body excitations, whose quantum coherence is strongly protected by symmetry and spectral detuning. Specifically, we theoretically demonstrate that small symmetric clusters of magnetic (rare-earth) ions in insulators can host strongly noise-resilient "qubits" that are characterized, and protected, by non-trivial irreducible representation of the spatial symmetries. We suggest that these cluster quantum excitations can serve as sensors for exotic many-body dynamics (spectral diffusion and quasi-many body localization).

Effective models are a useful tool to describe physical systems. To construct one, we identify a relevant low energy subspace and apply perturbation theory. While systematic, this procedure is cumbersome and time consuming when applied to high perturbative orders or with multiple perturbations. Here we develop an efficient algorithm to produce symbolic and numeric low energy models. Our algorithm is fast, versatile, and well tested. https://pymablock.readthedocs.io/en/latest/

The discovery of superconducting and correlated insulating behavior in twisted bilayer graphene (TBG) has shaken up the field of two-dimensional (2D) materials, reinvigorating the study of graphene-based systems. We demonstrate that one-dimensional moire patterns, analogous to those found in twisted bilayer graphene, can arise in collapsed chiral carbon nanotubes (CNT) [1]. Performing a detailed study of the electronic structure of all types of chiral nanotubes, previously collapsed via molecular dynamics and validated against ab-initio modeling, we find that magic angle physics occurs in all families of collapsed carbon nanotubes [2]. Velocity reduction, flat bands, and localization in AA regions with diminishing moire angle are revealed. Remarkably, all kinds of nanotubes behave the same with respect to magic angle tuning, giving rise to magic angles in full agreement with those of TBG. Superconductivity in TBG was an unexpected phenomenon, so the quest for other systems which could be the 1D analogues of TBG is of great importance to elucidate the nature of superconductivity found therein. Moreover, nontrivial topological phases have been found in the magic angle regime and are closely related to flat bands. Therefore, chiral collapsed carbon nanotubes stand out as promising candidates to explore topology and superconductivity in low dimensions, emerging as the one-dimensional analogues of twisted bilayer graphene. [1] O. Arroyo-Gascón, R. Fernández-Perea, E. Suárez Morell, C. Cabrillo, L. Chico, Nano Letters, 20, 7588 (2020). [2] O. Arroyo-Gascón, R. Fernández-Perea, E. Suárez Morell, C. Cabrillo, L. Chico, Carbon, 205, 394 (2023).

We study the scattering of two-dimensional massless Dirac fermions, charge carriers in monolayer graphene under ambient condition, from a two-dimensional array of Gaussian graphene quantum dots (QD) and compare the same with the diffraction process in optics. We subsequently calculate the d-c resistivity of such structure and extend our analysis to the QD lattices of different geometries as well as the moir\'e pattern of such QD lattice. The relevance of our theoretical calculations to experiments is also analysed in detail.

Quantum Hall junctions in graphene have recently been introduced as a novel platform for determining spin structure of ground states at various Landau level fillings via magnon transport. We introduce a model to study magnon scattering in skyrmion crystals, sandwiched between ferromagnets which act as the source of magnons. Skyrmions are topological objects while skyrmion crystals break internal and translational symmetries, thus our setup allows us to study the interplay of topology and symmetry breaking. Starting from a basis of holomorphic theta functions, we construct an analytical ansatz for such a junction with finite spatially modulating topological charge density in the central region and vanishing in the leads. We then construct a suitably defined energy functional for the junction and derive the resulting equations of motion, which resemble a Bogoliubov-de Gennes-like equation. Using analytical techniques, field theory, heuristic models and microscopic recursive transfer-matrix numerics, we calculate the spectra and magnon transmission properties of the skyrmion crystal. We find that magnon transmission can be understood via a combination of low-energy Goldstone modes and effective emergent Landau levels at higher energies. The former manifests in discrete low-energy peaks in the transmission spectrum which reflect the nature of the Goldstone modes arising from symmetry breaking. The latter, which reflect the topology, lead to band-like transmission features, from the structure of which further details of the excitation spectrum of the skyrmion crystal can be inferred. Such characteristic transmission features are absent in competing phases of the quantum Hall phase diagram, and hence provide direct signatures of skyrmion crystal phases and their spectra [1]. Our results directly apply to quantum Hall heterojunction experiments in monolayer graphene with the central region doped slightly away from unit filling, a $\nu=1:1 \pm \delta \nu:1$ junction and are also relevant to junctions formed by metallic magnets or in junctions with artificial gauge fields. Besides, purely SU(2) spin skyrmion crystals, we also study crystals of SU(4) entanglement skyrmions [2], in which the spin and valley degrees of freedom are entangled. We show how non-local transport signatures of magnons in such junction experiments detect and quantify such entanglement [3], thereby establishing magnon transport as a concrete route to probe entanglement in multicomponent quantum Hall systems. [1] Nilotpal Chakraborty, Roderich Moessner, and Benoit Doucot - In prep (2023). [2] Nilotpal Chakraborty, Roderich Moessner, and Benoit Doucot - “Riemann meets Goldstone: magnon scattering off quantum Hall skyrmion crystals probes interplay of symmetry break- ing and topology” - arXiv:2304.13049 (2023). [3] Benoıt Doucot et al. “Entanglement skyrmions in multicomponent quantum Hall systems” - Physical Review B 78.19 (2008)

We study the logarithmic entanglement negativity of symmetry-protected topological phases (SPTs) and quantum critical points (QCPs) of one-dimensional noninteracting fermions at finite temperatures. In particular, we consider a free fermion model which realizes not only quantum phase transitions between gapped topological phases but also an exotic topological phase transition between quantum critical states, namely the fermionic Lifshitz transition. We show that the bipartite entanglement negativity between two adjacent blocks of fermions sharply reveals the crossover boundary of the quantum critical fan near the QCP between the gapped phases. Along the critical phase boundary between the gapped phases, the sudden decrease in the entanglement negativity signals the fermionic Lifshitz transition responsible for the change in the topological nature of the QCPs. The high-temperature series expansion of the density operator shows that the entanglement negativity of every gapped and gapless state is converged to zero as $\sim T^−2$ in the high-temperature limit. We further demonstrate that the tripartite entanglement negativity between two spatially separated disjoint blocks of fermions can count the number of topologically protected boundary modes for both SPTs and topologically nontrivial QCPs at zero temperature. The long-distance entanglement between the boundary modes vanishes at finite temperatures due to the instability of SPTs protected by on-site symmetries.

We examine the possibility of Floquet engineering in candidate Kitaev materials. We give an approximation for heating processes arising from doublon holon propagation and find that compounds with stronger Hund's rule coupling are less prone to heating. We then investigate the impact of light frequency and amplitude on magnetic interaction terms up to third nearest neighbor and find that third neighbor Heisenberg coupling $J_3$ is very susceptible to tuning by circularly polarized light. The take hopping via ligands explicitly into account, which necessitates perturbation theory up to fourth-order. Finally, we investigate arbitrary polarization, going from linear to circular polarization via more complex Lissajous figures. Pascal Strobel and Maria Daghofer Phys. Rev. B 105, 085144 (2022); arXiv:2302.05296

Inspired by the experimental results on the spin-liquid candidate PbCuTe$_2$O$_6$ [1], we characterize the classical Heisenberg models on the distorted windmill lattice and discuss their applicability to this compound. The DFT calculations from this compound found antiferromagnetic Heisenberg couplings $J_n$ up to the fourth nearest neighbor, with $J_1$ almost equal to $J_2$. Taking this as a starting point, we discuss the role of $J_3$ and $J_4$ in determining the magnetic ground state, assuming $J_1=J_2$. We found that $J_3$ and $J_4$ are in competition between each other, opening interesting scenarios. The ratio $J_3\lessgtr J_4$ defines two distinct magnetically ordered ground states with a subextensive ground state manifold along the phase boundary, that becomes extensive at one special point in which all the four interactions are equal. In the case of extensive degeneracy, we uncover an unusual type of classical spin liquid defined on a lattice of corner sharing octahedra, with the underlying lattice formed by the octahedra being non-bipartite. Then, we fix the $J_n$ to the values proposed for PbCuTe$_2$O$_6$, and compare the classical model with the experimental results. In this case, the classical model exhibits a phase transition at finite temperature towards an incommensurate magnetically ordered ground state, that was not observed for PbCuTe$_2$O$_6$. This indicates that quantum fluctuations play an important role in determining the magnetic properties of this material. Finally, we simulated the dynamical structure factor for several temperatures. Our results show that the simulated structure factor in the paramagnetic regime agrees, to some extent, with the one from Inelastic Neutron Scattering experiments at very low temperature [1]. The broad spin-liquid features determined by quantum fluctuations found in experiments are overall well reproduced by thermal fluctuations. [1] Sharavani Chillal et al. \textit{Nat Commun}, \textbf{11}, 2348 (2020)

We report finite-size topology in the quintessential time-reversal (TR) invariant systems, the quantum spin Hall insulator (QSHI) and the three-dimensional, strong topological insulator (STI): previously-identified heli- cal or Dirac cone boundary states of these phases hybridize in wire or slab geometries with one open boundary condition for finite system size, and additional, topologically-protected, lower-dimensional boundary modes appear for open boundary conditions in two or more directions. For the quasi-one-dimensional (q(2-1)D) QSHI, we find topologically-protected, quasi-zero-dimensional (q(2-2)D) boundary states within the hybridization gap of the helical edge states, determined from q(2-1)D bulk topology characterized by topologically non-trivial Wilson loop spectra. We show this finite-size topology furthermore occurs in 1T’-WTe2 in ribbon geometries with sawtooth edges, based on analysis of a tight-binding model derived from density-functional theory calcula- tions, motivating experimental investigation of our results. In addition, we find quasi-two-dimensional (q(3-1)D) finite-size topological phases occur for the STI, yielding helical boundary modes distinguished from those of the QSHI by a non-trivial magneto-electric polarizability linked to the original 3D bulk STI. Finite-size topological phases therefore exhibit signatures associated with the non-trivial topological invariant of a higher-dimensional bulk, clearly distinguishing them from previously-known topological phases. Finally, we find the q(3-2)D STI also exhibits finite-size topological phases, finding the first signs of topologically-protected boundary modes of codimension greater than 1 due to finite-size topology. Finite-size topology of four or higher-dimensional systems is therefore possible in experimental settings without recourse to thermodynamically large synthetic dimensions.

Fünfhaus, Axel* Marius Möller, Thilo Kopp, Roser Valentí Email: fuenfhaus@itp.uni-frankfurt.de The Hall conductivity of insulating many-body systems can be expressed as a function of the many-body Chern number, which is defined over a closed manifold of twisted boundary conditions in real space related to charge transport via flux insertion. Making use of the magnetic translation algebra for quantum Hall systems one can prove [1] similarly to the noninteracting case that the many-body Chern number $C$ is restricted by the relation $e^{2\pi i (C p/q - \rho)} = 1$, with particle density \rho and flux quantum ratio $p/q$. We scrutinize the physical implications of this theorem by taking into account the role of spontaneous symmetry breaking for topological phase transitions and numerically investigate interacting quantum Hall phases that can realize trivial insulating phases, despite the preservation of the magnetic translation symmetry. [1] A. Matsugatani et al., Physical Review Letters, 120, 096601 (2018) Acknowledgments: This work is supported by the Deutsche Forschungsgemeinschaft (DFG) through QUAST-FOR5249 - 449872909 (project TP4)

Strongly degenerate eigenspaces are an exciting phenomenon in spin glasses, spin ice, and topologically-degenerate quantum systems. We demonstrate how to construct models with a high degree of degeneracy from one of the most prominent classes of many-body systems which is partially amenable to exact solutions, the $XXZ$ Heisenberg models. Starting with quantum spins attached to the vertices of an arbitrary graph, we reverse engineer $XXZ$ models, also with additional on-site magnetic fields and Dzyaloshinskii–Moriya interactions, that support simple product states as eigenstates. Sufficient conditions for product states to be eigenstates can be graphically represented yielding rules reminiscent of Kirchhoff's laws for electrical circuits. The graphical rules imply a construction procedure for a yet unknown class of potentially strongly degenerate spin models. For some of these models, the product eigenstates turn out to span a large degenerate eigenspace whose dimension scales exponentially with the number of spins. The singular nature of these eigenspaces hints at an intriguing connection between lattice topology, degeneracy and entanglement.

The emerging field of Cavitronics aims at enabling the control of collective phenomena in cavity-embedded solid-state platforms, purely through the interaction with the engineered electromagnetic quantum ground state. I will present an experiment aimed at assessing the modification of the quantized Hall resistance in a two-dimensional electron gas via the vacuum fields of a complementary split-ring resonator. By developing an on-chip Wheatstone bridge, we can measure deviations from quantization down to 1 part in $10^5$. Although in the limit of zero temperature we recover the exact quantization, we have observed how the cavity can modify the transport in the Hall states when the temperature is increased.

The salient property of the electronic band structure of twisted bilayer graphene (TBG), at the so-called magic angle (MA), is the emergence of flat bands around the charge neutrality point. These bands are associated with the observed superconducting phases and the correlated insulating states. Scanning tunneling microscopy combined with angle resolved photoemission spectroscopy are usually used to visualize the flatness of the band structure of TBG at the MA. Here, we theoretically argue that spin pumping (SP) provides a direct probe of the flat bands of TBG and an accurate determination of the MA. We consider a junction separating a ferromagnetic insulator and a heterostructure of TBG adjacent to a monolayer of a transition metal dichalcogenide. We show that the Gilbert damping of the ferromagnetic resonance experiment, through this junction, depends on the twist angle of TBG, and exhibits a sharp drop at the MA. We discuss the experimental realization of our results which open the way to a twist switchable spintronics in twisted van der Waals heterostructures.

Correlation-driven gapless topological phases are a vastly unexplored field of great current interest. In a joint effort of experiment [1,2] and theory [3], the Weyl-Kondo semimetal state in the heavy fermion material Ce$_3$Bi$_4$Pd$_3$ was recently established as a prime example. A cubic-in-temperature contribution to the electronic specific heat [1] and a giant spontaneous Hall effect [3] are extreme topological responses attributed to the presence of Weyl nodes in the immediate vicinity of the Fermi level. To advance the field and understand the stabilization principles of these phases, it is important to identify other candidate materials. One strategy is to search for novel topological phases in the vicinity of quantum critical points. A unique material to test this approach is the noncentrosymmetric Kondo semimetal CeRu$_4$Sn$_6$. It was theoretically proposed to be a correlated Weyl semimetal [4] and shows quantum critical behavior without any form of parameter tuning [5]. Here we perform magnetotransport and specific heat measurements under hydrostatic pressure, in search for signatures of Weyl-Kondo physics emerging across the p-B-T phase diagram of CeRu$_4$Sn$_6$. [1] S. Dzsaber et al., Phys. Rev. Lett., 118, 246601 (2017) [2] S. Dzsaber et al., Proc. Natl. Acad. Sci. U.S.A. 118, e2013386118 (2021) [3] H.-H. Lai et al., Proc. Natl. Acad. Sci. U.S.A. 115, 93 (2018) [4] Y. Xu et al., Phys. Rev. X 7, 011027 (2017) [5] W. T. Fuhrman et al., Sci. Adv. 7, eabf9134 (2021) * The work in Vienna was supported by the Austrian Science Fund (FWF grants I4047, P29279, and I5868-N/FOR 5249 "QUAST"), the European Microkelvin Platform (H2020 project 824109), and the European Research Council (ERC Advanced Grant 101055088-CorMeTop). In collaboration with: D. A. Zocco$^1$, F. Mazza$^{1,2}$, A. M. Strydom$^3$, J. Larrea J.$^1$, X. Yan$^1$, A. Prokofiev$^1$, and S. Paschen$^1$ $^1$Institute of Solid State Physics, Vienna University of Technology, 1040 Vienna, Austria $^2$Institut Laue-Langevin, Grenoble Cedex 9, France $^3$Physics Department, University of Johannesburg, Auckland Park 2006, South Africa

Strongly correlated electron systems remain at the forefront of current research, with heavy fermion compounds being highly tunable representatives. They can typically be driven across various types of quantum critical points, by readily accessible values of non-thermal tuning parameters. Of particular interest is the situation where the quantum critical fluctuations go beyond those of a vanishing Landau order parameter, for instance via the phenomenon of Kondo destruction [1]. Ce3Pd20Si6 is a heavy fermion compound that undergoes a sequence of two such quantum critical transitions [2,3,4]. With the ultimate goal of studying the thermal conductivity and scrutinizing the validity of the Wiedemann-Franz law across both these QCPs, we will present first thermal conductivity measurements on this material to very low temperatures. In zero magnetic field, we investigate the contributions due to both the antiferroquadrupolar and the antiferromagnetic phase transition. Understanding their temperature and magnetic field dependence will be essential to draw firm conclusions. [1] Paschen, S. & Si, Q., Nat. Rev. Phys. 3, 9 (2021) [2] Custers, J., et al., Nature Mater 11, 189-194 (2012) [3] Ono, H., et al., J. Phys. Condens. Matter 25, 126003 (2013) [4] Martelli, V. et al., Proc. Natl. Acad. Sci. 116, U.S.A. 116, 17701-17706 (2019 The work in Vienna was supported by the European Microkelvin Platform (H2020 project 824109) and the Austrian Science Fund (FWF-I5868-N - FOR 5249 - QUAST and FWF SFB F 86, Q-M&S).

Confining two-dimensional Dirac fermions is a conceptual and practical challenge. It can be achieved, in principle, by introducing magnetism to the surfaces of a topological insulator, or in Graphene using intricate techniques of fabrications, electrostatic gating, and coupling to superconductivity. However, these are all complex methods that require external fields or materials. In this work, we show that Dirac fermion confinement appears naturally on the surfaces of topological crystalline insulators (TCIs), which host multiple surface Dirac cones, depending on the surface terminations and the symmetries they preserve or break. This confinement is most dramatically reflected in the flux dependence of the surface states of a TCI in a nanowire geometry, where different facets of the wire connect to form a closed surface. Using SnTe as a case study, we show how wires with all four facets of the <100> type display novel Aharonov-Bohm oscillations that imply an extended nature of the surface states. In nanowires with four facets of the <110> type, such oscillations are absent due to the strong confinement of the Dirac states to each facet separately. Our results place TCI nanowires as a versatile platform for confining and manipulating Dirac surface states.

We formulate a Landau theory for altermagnets, a class of colinear compensated magnets with spin-split bands. Starting from the non-relativistic limit, this Landau theory goes beyond a conventional analysis by including spin-space symmetries, providing a simple framework for understanding the key features of this family of materials. We find a set of multipolar secondary order parameters connecting existing ideas about the spin symmetries of these systems, their order parameters and the effect of non-zero spin-orbit coupling. We account for several features of canonical altermagnets such as RuO2, MnTe and CuF2 that go beyond symmetry alone, relating the order parameter to key observables such as magnetization, anomalous Hall conductivity and magneto-elastic and magneto-optical probes.

The breakdown of the lattice Kondo effect in local-moment metals can lead to nontrivial forms of quantum criticality and a variety of non-Fermi-liquid phases. Given indications that Kondo-breakdown transitions involve criticality not only in the spin but also in the charge sector, we investigate the interplay of Kondo breakdown and strong valence fluctuations in generalized Anderson lattice models. We employ a parton mean-field theory to describe the transitions between deconfined fractionalized Fermi liquids and various confined phases. We find that rapid valence changes near Kondo breakdown can render the quantum transition first order. This leads to phase-separation tendencies which, upon inclusion of longer-range Coulomb interactions, will produce intrinsically inhomogeneous states near Kondo-breakdown transitions. We connect our findings to unsolved aspects of experimental data.

In this study, we explore the coupling between microwave photons and magnon modes in a Cuprate antiferromagnetic material with four sublattices. Using a single-photon cavity setup, we calculate the strength of the coupling and investigate the resulting entanglement between the different modes, including magon-magnon and magnon-photon. Our analysis reveals significant entanglement among the magnon modes, while the entanglement between the photons and magnons remains negligible. Interestingly, the coupling with cavity photons amplifies the magnon mode entanglement, with maximum enhancement observed at resonance. This work contributes to the understanding of entanglement dynamics in complex quantum systems and has implications for applications such as magnon cooling and cavity spintronics.

Two dimensional cohererent spectroscopy (2DCS) is a powerful tool, probing the nonlinear optical response of correlated systems. % An interesting application of this tool is in probing fractionalized excitations in quantum phases of matter, which are challenging to distinguish unambiguously in linear response. % Frustrated rare-earth pyrochlore oxides, R$_2$M$_2$O$_7$, have long been of interest as potential realizations of fractionalized quantum phases, and the application of 2DCS to these systems has the potential to bring new insight into the nature of their excitations. % Here we present theoretical predictions for the 2DCS response of rare-earth pyrochlore magnets subject to a $[110]$ magnetic field. % This field direction is of particular interest because it splits the system into a set of effective 1-dimensional spin chains. % This enables a controlled theoretical approach to the problem, while retaining fractionalized excitations in the spectrum. % We present two worked examples, based on the modelling of real materials, Ce$_2$Zr$_2$O$_7$ and Nd$_2$Zr$_2$O$_7$. % The resulting spectra give sensitive information about the microscopic coupling paraneters of the system. % We show how the use of different photon polarizations in the 2DCS experiment can be used as a filter to either pick out fractionalized spinons or conventional spin waves from the spectrum. % We further use numerical calculations to demonstrate the robustness of the key features in the response to non-integrable terms in the microscopic Hamiltonian. % We thereby establish a set of predictions for the use of 2DCS in exploring frustrated interactions and complex magnetic states in real materials of present interest.

While topological superconductors are rare in naturally-occurring compounds, they may be realised by appropriately designing quantum materials. In particular, lattices of Yu-Shiba-Rusinov bound states – Shiba lattices – that arise when magnetic adatoms are placed on the surface of a conventional superconductor can be used to create topological bands within the superconducting gap of the substrate. By means of scanning tunnelling microscopy, adatom lattices can be assembled and probed with single atom precision. The experimentally realised structures reveal two signatures consistent with two types of mirror symmetry protected topological superconductivity, with (i) edge modes and higher-order corner states, and (ii) symmetry-protected bulk nodal points. We present a theoretical analysis indicating how the topological character and boundary modes of such structures should be protected by the spatial symmetries of the adatom lattice.

Chains of magnetic adatoms on superconductors have been discussed as promising systems for realizing Majorana end states. Here, we show that dilute Yu-Shiba-Rusinov (YSR) chains are also a versatile platform for quantum magnetism and correlated electron dynamics, with widely adjustable spin values and couplings. Focusing on subgap excitations, we derive an extended t− J model for dilute quantum YSR chains and use it to study the phase diagram as well as tunneling spectra. We explore the implications of quantum magnetism for the formation of a topological superconducting phase, contrasting it to existing models assuming classical spin textures.

We investigate the time evolution of the second-order Rényi entropy (RE) for bosons in a one-dimensional optical lattice following a sudden quench of the hopping amplitude $J$. Specifically, we examine systems that are quenched into the strongly correlated Mott-insulating (MI) regime with $J/U\ll 1$ ($U$ denotes the strength of the on-site repulsive interaction) from the MI limit with $J=0$. In this regime, the low-energy excited states can be effectively described by fermionic quasiparticles known as doublons and holons. They are excited in entangled pairs through the quench dynamics. By developing an effective theory, we derive a direct relation between the RE and correlation functions associated with doublons and holons. This relation allows us to analytically calculate the RE and obtain a physical picture for the RE, both in the ground state and during time evolution through the quench dynamics, in terms of doublon-holon pairs. In particular, we show that the RE is proportional to the population of doublon-holon pairs that span the boundary of the subsystem. Our quasiparticle picture introduces some remarkable features that are absent in previous studies on the dynamics of entanglement entropy in free-fermion models. It provides with valuable insights into the dynamics of entanglement entropy in strongly-correlated systems.

Recent experiments involving Co-based d$^7$ honeycomb materials have heightened interest in XXZ models with complex interactions extending beyond the nearest neighbor exchange. In this presentation, I will discuss our latest findings on the quantum phase diagram of the spin 1/2 J$_1$-J$_2$-J$_3$ honeycomb model with XXZ-type anisotropy. We employed exact diagonalization and pseudo-fermion functional renormalization group methods to accurately map out the ground states across a broad parameter range, discovering a variety of phases such as incommensurate spirals, out-of-plane Ising order, and quantum disordered phases. Specifically, we have identified possible states of a gapless quantum spin liquid phase near the Heisenberg limit.

The one-dimensional spin-1/2 Heisenberg model with antiferromagnetic exchange coupling is one of the best studied systems in quantum magnetism. The ground state of the isolated chain is a Luttinger liquid with critical spin and dimer correlations. It is an open question how these properties are affected by a coupling to the environment. In this talk, we consider the effects of local site and bond dissipation on the quantum spin chain. Using a recently developed quantum Monte Carlo method for retarded interactions, we first show that ohmic site dissipation spontaneously breaks the SO(3) spin symmetry and induces long-range antiferromagnetic order in the 1D chain beyond the applicability of the Mermin-Wagner theorem. Ohmic site dissipation is a marginally relevant perturbation so that exponentially large system sizes are required to observe long-range order at small couplings. Below this length scale, our numerics is dominated by a crossover regime where spin correlations show different power-law behaviors in space and time. Secondly, we study the effects of bond dissipation as a function of the interaction range of the corresponding retarded interaction. For a slow power-law decay, we find that bond dissipation immediately induces valence-bond-solid order, whereas for a fast decay the critical phase remains stable up to a critical coupling. We discuss the properties of the critical phase and the quantum phase transition under the influence of the dissipative bath.

We devise a generic and experimentally accessible recipe to prepare boundary states of topological or non-topological quantum systems through an interplay between coherent Hamiltonian dynamics and local dissipation. Intuitively, our recipe harnesses the spatial structure of boundary states which vanish on sublattices where losses are suitably engineered. This yields unique non-trivial steady states that populate the targeted boundary states with infinite life times while all other states are exponentially damped in time. Remarkably, applying loss only at one boundary can yield a unique steady state localized at the very same boundary. We detail our construction and rigorously derive full Liouvillian spectra and dissipative gaps in the presence of a spectral mirror symmetry for a one-dimensional Su-Schrieffer-Heeger model and a two-dimensional Chern insulator. We outline how our recipe extends to generic non-interacting systems (arXiv:2305.00031).

Topological bands with a flat dispersion host strongly correlated states with or without intrinsic topological orders. The kinetic part of the system is trivial and the system is dominated by the interaction. At a first glance, electrons do not have any preference to occupy in the Brillouin zone. Despite the featureless kinetic dispersion, topological bands are usually equipped with nontrivial band geometry. We show that the nonuniform band geometry gives rise to emergent Fermi surfaces and it leads to a general particle-hole asymmetry. The electrons tend to fill regions in the Brillouin zone where their quantum distance is shorter. The emergent Fermi surface transforms the strongly interacting problem to a weakly interacting one. This dictates the low-energy physics and serves as a guiding principle for potential symmetry-breaking states. We show that in moiré materials, the quantum distance can be well approximated by a local quantity called the quantum metric. From this simple quantity, we can deduce what phases are favoured in different moiré systems at fractional fillings.