Korrelationstage 2023

While topology has found multifold applications in linear band theory, its relevance for nonlinear systems remains to be explored. In my talk, I will investigate the existence, stability, and symmetry of localized breather modes (standing solitary waves) in Bose-Einstein condensates or photonic crystals with Kerr nonlinearity. Using an exactly solvable 'molecular breather limit', I will analytically predict the breather spectrum in two nontrivial examples inspired from topological band theory: the nonlinear 1D Su-Schrieffer-Heeger model protected by inversion symmetry, and a nonlinear 2D obstructed atomic insulator protected by $\mathcal{C}_3$ rotational symmetry. I will end my talk by presenting numerical results that confirm the validity of our analytical predictions away from the exactly solvable limit.

In recent years, topological magnetic materials have received significant attention in the field of condensed matter physics due to their potential for both fundamental research and technological applications. The search for new topologically non-trivial materials has been revolutionized by the formalism of topological quantum chemistry, which maps the symmetry properties of bands to topological properties. Building upon previous research, we conducted a high-throughput search for topological magnetic materials on new experimentally reported commensurate magnetic structures from MAGNDATA, doubling the number of available materials on the Topological Magnetic Materials database. For each material, we performed first-principle electronic calculations and diagnosed the topology as a function of the Hubbard U parameter. Our high-throughput calculation led us to the prediction of 502 previously overlooked experimentally relevant topologically non-trivial materials. We present four remarkable examples of these materials, each showcasing a different topological phase: CaMnSi, a narrow gap axion insulator, Mn2AlB2, which exhibits a nodal line semimetal to topological insulator transition, FeCr2S4, a symmetry-enforced semimetal with double Weyls, and CsMnF4, a material presenting a new type of quasi-symmetry protected closed nodal surface. Our results demonstrate the power of symmetry-based diagnosis to predict new topological phases of matter in realistic materials.

Interacting fermion ladders are important platforms to study quantum phases of matter including various Mott insulators with different symmetry properties, such as the D-Mott and S-Mott phase. The latter hold pre-formed electron pairs and become paired liquids (d-wave and s-wave) upon doping. These Mott insulators were believed to be distinct phases (see e.g. the classical textbook "Quantum physics in one dimension"). We demonstrate that this understanding is incomplete: They are in fact two facets of the same interaction-induced topological phase. With this, we provide a quantum analog of the well-known terminable liquid-gas transition. However, the phenomenology we uncover is even richer, as in contrast to the liquid-gas transition, the order of the transition can be tuned by the interaction and bears relevance for the topological properties of the system. These results show interesting synergy between fundamental questions in the fields of fermion pairing, topology, Mott insulators and terminated phase transitions.

We study a generic model of a Chern insulator supplemented by a Hubbard interaction in arbitrary even dimension $D$ and demonstrate that the model remains well defined and nontrivial in the $D\to\infty$ limit. Dynamical mean-field theory is applicable and predicts a phase diagram with a continuum of topologically different phases separating a correlated Mott insulator from the trivial band insulator. We discuss various features, such as the elusive distinction between insulating and semimetal states, which are unconventional already in the noninteracting case. Topological phases are characterized by a nonquantized Chern density replacing the Chern number as $D\to\infty$.

To this day, quantum spin ice remains perhaps the most important example of a quantum spin liquid in three dimensions, owing to (i) the plethora of pyrochlore compounds which might realize this phase, and (ii) the detailed theoretical understanding of the classical nearest-neighbor spin ice (NNSI) model and how quantum perturbations of this model can be mapped to a U(1) lattice gauge theory. In this talk, I propose the existence of a new class of gapless spin liquids in three dimensions: 2-form U(1) quantum spin liquids. To illustrate this phase, we first introduce a minimal classical Ising model on the pyrochlore lattice, analogous to NNSI, which we dub the "spin vorticity model", constructed to enforce a local zero-curl constraint on every hexagonal loop of the lattice. We demonstrate using analytic approximation and numerical Monte Carlo simulations that this model has an extensive ground state entropy and a low-temperature Coulomb-like phase characterized by "inverted" pinch points. We give a detailed characterization of the emergent gauge structure of the ground state manifold of this model, which may be described as a condensate of membranes---flipping a collection of spins forming a closed surface costs zero energy. Unlike established spin liquids like NNSI, this model contains no point-like quasiparticle excitations. Instead, the excitations are extended string objects, created by flipping a collection of spins forming an open surface. At finite temperature, the classical model is then described by a gas of string loops in a background of fluctuating membranes. We then introduce a minimal quantum extension of the spin vorticity model, from which we derive an effective membrane exchange model of the quantum dynamics within the classical ground state manifold, which we map to a frustrated 2-form U(1) lattice gauge theory. We further demonstrate how to quantize the string excitations, by coupling a 1-form string field to the emergent 2-form U(1) gauge field, thus mapping a spin model to a 2-form gauge-Higgs model. We discuss the stability of the gapless deconfined phase of this gauge theory, and thus the possibility of realizing a novel phase of quantum matter: a 2-form U(1) quantum spin liquid.

We investigate the interplay between the different interaction channels within a simplified model with Hubbard interaction and the chemical potential tuned to a single Van Hove singularity. Since the particle-hole fluctuations diverge at VHS point, the system is expected to become ferromagnetic at mean-field level. However, there is interference from particle-particle channel, which suppresses this tendency by screening the interaction in ferromagnetic channel. As the leading instability, a superconducting spin-triplet state is stabilized by particle-hole fluctuations. The momentum-structure of the triplet order parameter is unusual, as the nodal region is found to be exponentially small as a function of the interaction strength.

Heterostructures of transition metal dichalcogenides (TMDs) allow for realizing controllable and strongly interacting mixtures of excitons and holes. Thus they are ideal platforms for investigating unconventional states of matter, such as superconductivity. Remarkably, the selective nature of bound states in certain TMDs, for example MoX2, allows us to describe the relevant physics as bosonic excitons interacting with spinless charge carriers. Consequently, only triplet superconductivity can be achieved in these materials. The key mechanism in the experimental setup we propose, is then provided by Feshbach resonances, which can be realized by tuning an external perpendicular electric field. Tuning the field brings the open channel in resonance with the intermediate bound state of an exciton and the charge carrier, which is also known as a trion. This in turn tunes the interactions between excitons and charge carriers and manipulates the strength of the superconducting order parameter. This mechanism enables an order-of-magnitude enhancement in the order parameter. We numerically study the nature of the triplet superconductor and find that it is dominated by p-wave with a zero-temperature topological px+ ipy superconductivity. Additionally, we discuss the experimental signatures associated with this type of non-trivial topological phase. Through our proposal, we demonstrate the potential of TMD heterostructures as a tunable platform for realizing p-wave topological superconductivity.

In research labs worldwide, quantum physics is making unprecedented strides. The realization of robust quantum systems holds tremendous promise for applications in secure communication and computing. Yet, as physicists, our most exciting pursuit lies in experimentally testing quantum phenomena predicted over the past century within highly controlled environments. In this colloquium, I will explore two distinct approaches to engineering quantum matter: one fueled by human creativity and the other driven by artificial intelligence. Throughout the colloquium, we will uncover how these approaches can be effectively deployed in contemporary quantum experiments, paving the way for advancements in our understanding and control of quantum phenomena.

Quantum Spin Liquids (QSL) have recently enjoyed renewed interest. This is partly driven by synergies with quantum information theory and by the experimental progress, which provides evidence for new material realizations, in particular in 2D van-der-Waals materials. The chemical versatility of this platform allows for and requires the study of new probes in device geometries combining QSLs with, e.g., metals or semimetals. In this talk, I will discuss all-electrical probes for gapless spinons in tunneling [1] and, in more detail, electrical drag signatures of QSL sandwich heterostructures [2]. Finally, I will discuss bulk 4Hb-TaS2, which is a layered material consisting of QSL and metallic layers, and I will attempt to provide theoretical insight into its unconventional superconducting properties. [1] EJ König, MT Randeria, B Jäck; Physical Review Letters 125 (26), 267206 (2020) [2] R Mazzilli, A Levchenko, EJ König; arXiv:2211.08421. [3] EJ König, in preparation.

One of the most famous quantum systems with topological properties, the spin S=1 antiferromagnetic Heisenberg chain, is well-known to display exotic S=1/2 edge states. However, this spin model has not been analyzed from the more general perspective of strongly correlated systems varying the electron-electron interaction strength. Here we report the numerical investigation of the emergence of the Haldane state and its edge modes in a system of interacting electrons - the two-orbital Hubbard model - with increasing repulsion strength U. We show that these interactions not only form the magnetic moments but also form a topologically nontrivial fermionic many-body ground-state with zero-energy edges states that only at very large U converge to the Haldane chain model. Specifically, upon increasing the strength of the Hubbard repulsion and Hund exchange, we identify a novel sharp transition point separating topologically trivial and nontrivial ground-states. Surprisingly, the latter appears already at rather small values of the interaction U, in a regime where the magnetic moments are barely developed, thus generalizing the ideas of Haldane for S=1 spin Heisenberg models into previously unexplored territory involving delocalized electrons. Furthermore, our results indicate that the topological regime can be described by a liquid valence bonds state down to interaction strength of the order of the bare kinetic energy.

Condensation of bosons in Bose-Einstein condensates or Cooper pairs in superconductors refers to a macroscopic occupation of a few single-or two-particle states. A condensate is called “fragmented” if not a single, but multiple states are macroscopically occupied. While fragmentation is known to occur in particular Bose-Einstein condensates, we propose that fragmentation naturally takes place in striped superconductors. To this end, we investigate the nature of the superconducting ground state realized in the two-dimensional t−t′ Hubbard model as observed in DMRG. In the presence of charge density modulations, the condensate is shown to be fragmented and composed of partial condensates located on the stripes. The fragments of the condensates hybridize to form an extended macroscopic wave function across the system. We demonstrate that the fragments of the condensates are described by a simple intertwined Ginzburg Landau theory and discuss the relation and experimental predictions for the cuprate superconductors.

The pseudogap phase in cuprate superconductors is one of the most intriguing challenges in the theory of high temperature superconductivity. In this talk we elaborate on the hypothesis that pseudogap phenomena are mostly due to strong magnetic fluctuations. Using the two-dimensional Hubbard model to describe the electrons in the copper-oxygen planes of the cuprates, a gauge theory of fluctuating magnetic order is formulated and analyzed [1]. The theory is based on a fractionalization of electrons in fermionic chargons with a pseudospin degree of freedom and bosonic spinons, which leads to a SU(2) gauge redundancy. The chargons undergo Neel or spiral magnetic order below a density dependent transition temperature $T^*$. Fluctuations of the spin orientation are described by a non-linear sigma model obtained from a gradient expansion of the spinon action. The spin stiffnesses are computed from a renormalization group improved random phase approximation. The spinon fluctuations prevent magnetic long-range order of the electrons at any finite temperature. The phase with magnetic chargon order exhibits many features characterizing the pseudogap regime in high-Tc cuprates: a strong reduction of charge carrier density, a spin gap, and Fermi arcs. A substantial fraction of the pseudogap regime exhibits electronic nematicity. [1] P. M. Bonetti and W. Metzner, Phys. Rev. B 106, 205152 (2022).

Quantum oscillation phenomena describe the periodic variation of thermodynamic and transport properties of materials as a function of magnetic field. Since their discovery in 1930, their observation is commonly assumed to be a definite sign for the presence of a Fermi surface (FS) in a metal. Indeed, the effect forms the basis of a well-established experimental procedure for accurately measuring FS topology and geometry of metallic systems. In this talk I will discuss recent developments which challenge the canonical description of quantum oscillations. I will first review our work on quantum oscillations in insulators. Next, I will discuss the possibility of sharp quantum oscillation frequencies in metals which do not correspond to Fermi surface orbits and the effect of strong electron interactions. Finally, I will present experimental results confirming our theoretical predictions and discuss the broader implications of anomalous quantum oscillations.

Many proposals to realize topological superconductivity rely on exploiting the properties of a topologically trivial superconductor through the proximity effect. An alternate route is to search for systems where the pairing interaction directly gives rise to topologically non-trivial superconductivity. We argue that magnon-mediated superconductivity in heterostructures of transition metal dichalcogenides (TMDs) coupled to magnetic insulators provides a promising route to this end. Considering an antiferromagnetic insulator sandwiched between two TMDs, magnons in the antiferromagnetic insulator can mediate an interaction between electrons in the two TMDs. We show that this interaction can give rise to topologically non-trivial interlayer superconductivity. Co-authors: Joel Hutchinson, Jelena Klinovaja, Daniel Loss

We show that low-energy excitations in antiferromagnetic skyrmion phases on the triangular lattice are described by magnons dressed with an emergent SU(3) gauge field. Magnons can contribute to anomalous transports by feeling an emergent gauge field arising from noncoplanar spin textures and asymmetric exchange interactions. Most previous studies have relied on a U(1) gauge field picture where magnons have no internal degrees of freedom, which can explain the recent experimental results of the thermal Hall conductivity in the ferromagnetic skyrmion phase of $GaV_4Se_8$. However, in an antiferromagnetic skyrmion phase observed in $MnSc_2S_4$, the conventional U(1) gauge field description is no longer valid due to their antiferromagnetic three-sublattice structure. Here, we show that the antiferromagnetic three sublattices serve as internal degrees of freedom of magnons, and the associated SU(3) gauge field is naturally born from the slowly varying magnetic moments on three sublattices. We also demonstrate that the non-commutative nature of the SU(3) gauge field leads to qualitatively distinct transport properties from those predicted by the U(1) gauge field picture.

One of the most important practical hallmarks of topological matter is the presence of topologically protected, exponentially localised edge states at interfaces of regions characterised by unequal topological invariants. I will discuss that even when driven far from their equilibrium ground state, Chern insulators can inherit topological edge features from their parent Hamiltonian. In particular, the asymptotic long-time approach of the non-equilibrium steady state, governed by a Lindblad Master equation, can exhibit edge-selective extremal damping. This phenomenon derives from edge states of non-Hermitian extensions of the parent Chern insulator Hamiltonian. The combination of (non-Hermitian) topology and dissipation hence allows to design topologically robust, spatially localised damping patterns.

In thermal equilibrium the dynamics of phase transitions is largely controlled by fluctuation-dissipation relations: On the one hand, friction suppresses fluctuations, while on the other hand the thermal noise is proportional to friction constants. Out of equilibrium, this balance dissolves and one can have situations where friction vanishes due to antidamping in the presence of a finite noise level. We study a wide class of $O(N)$ field theories where this situation is realized at a phase transition, which we identify as a critical exceptional point. In the ordered phase, antidamping induces a continuous limit cycle rotation of the order parameter with an enhanced number of 2N−3 Goldstone modes. Close to the critical exceptional point, however, fluctuations diverge so strongly due to the suppression of friction that in dimensions d<4 they universally either destroy a preexisting static order, or give rise to a fluctuation-induced first order transition. This is demonstrated within a non-perturbative approach based on Dyson-Schwinger equations for N=2, and a generalization for arbitrary N, which can be solved exactly in the long wavelength limit. While this phenomenology is realised in nonreciprocally coupled active matter systems, we show that in order to realize this physics it is not necessary to drive a system far out of equilibrium: Using the peculiar protection of Goldstone modes, the transition from an xy magnet to a ferrimagnet is governed by an exceptional critical point once weakly perturbed away from thermal equilibrium.

Modern time-resolved spectroscopy experiments on quantum materials raise the question, how strong electron-electron interactions, in combination with periodic driving, form unconventional transient states. Here we show using numerically exact methods that in a driven strongly interacting charge-density-wave insulator a band-like resonance in the gap region is formed. We associate this feature to the so-called Villain mode in quantum-magnetic materials, which originates in moving domain walls induced by the interaction. We do not obtain the in-gap band when driving a non-interacting charge density wave model. In contrast, it appears in the interacting system also in equilibrium at intermediate temperatures and in the short-time evolution of the system after a quantum quench to the lowest-order high-frequency effective Floquet Hamiltonian. Our findings connect the phenomenology of a periodically driven strongly correlated system and its quench dynamics to the finite-temperature dynamical response of quantum-magnetic materials and will be insightful for future investigations of strongly correlated materials in pump-probe setups.

Predicting the fate of an interacting system in the limit where the electronic bandwidth is quenched is often highly non-trivial. The complex interplay between interactions and quantum fluctuations driven by the band geometry can drive a competition between various ground states, such as charge density wave order and superconductivity. In this work, we study an electronic model of topologically-trivial flat bands with a continuously tunable Fubini-Study metric in the presence of on-site attraction and nearest-neighbor repulsion, using numerically exact quantum Monte Carlo simulations. By varying the electron filling and the spatial extent of the localized flat-band Wannier wavefunctions, we obtain a number of intertwined orders. These include a phase with coexisting charge density wave order and superconductivity, i.e., a supersolid. In spite of the non-perturbative nature of the problem, we identify an analytically tractable limit associated with a `small' spatial extent of the Wannier functions, and derive a low-energy effective Hamiltonian that can well describe our numerical results.

Recent advances in the characterization and manipulation of van der Waals materials have shown that bilayers offer a unique platform for studying strongly correlated physics in two-dimensions (2D). Bilayers are different from monolayers in two important respects: the presence of hybridization due to interlayer hopping, and the existence of the long-range interactions between electrons in both the intra- and inter-layer channels, which differ only slightly. We study interaction effects using perturbation theory for the electronic charge susceptibility. We find that the susceptibility has peaks arising from scattering across the Fermi surfaces, not seen in the usual Lindhard function. In a conventional 2D electron gas, such peaks are suppressed by screening. In a bilayer system, however, we find that these peaks give rise to an enhanced response of out-of-plane dipoles to local potential differences across the layers. This response is not diminished by screening or interlayer hopping and becomes larger in the low-density limit.

Recent experimental advances of quantum simulators, as well as solids, allow unprecedented microscopic studies of the structure of strongly correlated quantum matter. In the Fermi-Hubbard model, believed to underly high-Tc superconductivity and accessible to ultracold atom experiments, this allows to study the origins of unconventional pairing from a microscopic perspective. In contrast to most analytical approaches, which start from high doping or weak coupling, we will take a strong coupling perspective and start from a strongly correlated Hubbard model at half filling. After reviewing widely established facts about the properties of Cooper pairs in high-Tc superconductors, I will analyze tightly bound pairs of charges in a Néel state in microscopic detail. I will argue that, even though these tightly bound pairs to not constitute the charge carriers in high-Tc superconductors, they can play a decisive role for the latter, by mediating strongly attractive interactions between fermionic magnetic (or spin) polarons. These new attractive interactions arise close to a hypothetic Feshbach resonance, where the tightly bound pairs become lower in energy than Cooper pairs of polarons. In particular we will show how the d-wave pairing symmetry of the latter naturally arises from the internal structure of the tightly bound pairs.

A key step in unraveling the mysteries of materials exhibiting unconventional superconductivity is to understand the underlying pairing mechanism. While it is widely agreed upon that the pairing glue in many of these systems originates from antiferromagnetic spin correlations, a microscopic description of pairs of charge carriers remains lacking. In this talk, I will present state-of-the art numerical methods to probe the internal structure and dynamical properties of pairs of charge carriers in quantum antiferromagnets in four-legged cylinders. Exploiting the full momentum resolution in our simulations, we are able to distinguish two qualitatively different types of bound states: a highly mobile, meta-stable pair, which has a dispersion proportional to the hole hopping t, and a heavy pair, which can only move due to spin exchange processes and turns into a flat band in the Ising limit of the model. We find qualitatively good agreement with the semi-analytical geometric string theory. Based on the intuition gained with the geometric string theory, we introduce mixed-dimensional models, which exhibit binding energies of the order of the spin exchange J and highly mobile pairs, and can be realized using cold atoms in optical lattices. We moreover relate the pair spectral function to the properties of Fermi-Hubbard excitons and draw connections to the optical conductivity, thus enabling insights from and connections between theoretical models, quantum simulators, and solid state experiments.

The quantum critical properties of interacting fermions in the presence of disorder are still not fully understood. While it is well known that for Dirac fermions, interactions are irrelevant to the non-interacting infinite randomness fixed point, the problem remains largely open in the case of Majorana fermions which further display a much richer disorder-free phase diagram. Pushing the limits of DMRG simulations, we carefully examine the ground-state of a Majorana chain with both disorder and interactions. Building on appropriate boundary conditions and key observables such as entanglement, energy gap, and correlations, we strikingly find that the non-interacting Majorana IRFP is very stable against finite interactions, in contrast with previous claims.

First, I will describe a variational quantum eigensolver for the simulation of strongly-correlated quantum matter based on a multi-scale entanglement renormalization ansatz (MERA) and gradient-based optimization. Due to its narrow causal cone, the algorithm can be implemented on noisy intermediate-scale (NISQ) devices and still describe large systems. The number of required qubits is system-size independent and increases only to a logarithmic scaling when using quantum amplitude estimation to speed up gradient evaluations. Translation invariance can be used to make computation costs square-logarithmic in the system size and describe the thermodynamic limit. For the practical implementation, the MERA disentanglers and isometries are Trotterized, i.e., implemented as brickwall circuits. With a few Trotter steps, one recovers the accuracy of the full MERA. Results of benchmark simulations for various critical spin models establish a quantum advantage. Secondly, I will address the question of barren plateaus in the optimization of isometric tensor network states. Barren plateaus correspond to scenarios where the average amplitude of the cost function gradient decreases exponentially with increasing system size. This occurs, for example, for quantum neural networks. We found that, in systems with finite-range interactions, variational optimization problems for matrix product states, tree tensor networks, and MERA are free of barren plateaus. The derived scaling properties of gradient amplitudes establish trainability and bear implications for efficient initialization procedures. References: arXiv:2108.13401 - Q. Miao and T. Barthel, "A quantum-classical eigensolver using multiscale entanglement renormalization" arXiv:2303.08910 - Q. Miao and T. Barthel, "Convergence and quantum advantage of Trotterized MERA for strongly-correlated systems" arXiv:2304.00161 - T. Barthel and Q. Miao, "Absence of barren plateaus and scaling of gradients in the energy optimization of isometric tensor network states" arXiv:2304.14320 - Q. Miao and T. Barthel, "Isometric tensor network optimization for extensive Hamiltonians is free of barren plateaus"

I discuss our work in applying tensor-network methods to two-dimensional strongly correlated electron models. First, I discuss our adaptation of the finite-projected-entangled-pair-state algorithm (fPEPS) for the two-dimensional Hubbard model. This adaptation uses projected entangled pair operators (PEPOs), takes full advantage of SU(2) symmetry, carries out both local variational optimization and global gradient-based optimization of the PEPS, and implements a number of other optimizations, so that we can treat lattice of up to 8x8 with PEPS bond dimension of up to 8. I discuss the accuracy and performance of this algorithm and its effectiveness relative to other methods. Second, I discuss work applying the DMRG with integrated mode transformations to Hubbard-like models in general, applying it spcefically to a two-dimensional model of spinless fermions with nearest- and next-nearest-neighbor hopping and nearest-neighbor Coulomb repulsion. I discuss the accuracy, computational cost and performance of the method as well as the ground-state phase diagram of the spinless fermion model at half filling.

In this talk, I will show that neural quantum states based on very deep (4-16-layered) neural networks can outperform state-of-the-art variational approaches on highly frustrated quantum magnets. In particular, we use group convolutional neural networks (GCNNs), which allow us to impose all space-group symmetries and to target nontrivial symmetry sectors variationally. I will demonstrate the power of our method by obtaining state-of-the-art ground- and excited-state energies for the $J_1-J_2$ Heisenberg model on the square and the triangular lattices. I will also discuss GCNN studies of Heisenberg models on fullerene geometries, where we obtained the spectrum of low-lying excited states resolved by point-group symmetry. On larger fullerenes, these contain distinct “towers of states” akin to those expected in an ordered magnet: Indeed, we are able to reconstruct the corresponding “magnon operators” from the ground-state correlation functions, which show the gradual emergence of honeycomb-like Néel order as the degree of frustration reduces.

Within the reduced basis methods approach, an effective low-dimensional subspace of a quantum many-body Hilbert space is constructed in order to investigate, e.g., the ground-state phase diagram. The basis of this subspace is built from solutions of snapshots, i.e., ground states corresponding to particular and well-chosen parameter values. Here, we show how a greedy strategy to assemble the reduced basis and thus to select the parameter points can be implemented based on matrix-product-state (MPS) calculations. Once the reduced basis has been obtained, observables required for the computation of phase diagrams can be computed with a computational complexity independent of the underlying Hilbert space for any parameter value. We illustrate the efficiency and accuracy of this approach for different one-dimensional quantum spin-1 models, including anisotropic as well as biquadratic exchange interactions, leading to rich quantum phase diagrams.

When two layers of graphene are stacked on top of each other with a finite relative angle of rotation, a moiré pattern forms. Most strikingly, at so-called “magic angles”, the largest of which is around 1 degree, the bands around the Fermi surface flatten significantly; this enhances the density of states and the impact of electron-electron interactions. Soon after the experimental discovery in 2018 that this enhancement can induce superconductivity and other, including magnetic, instabilities, it became clear that twisted bilayer graphene is only one example of an engineered van der Waals moiré system with a complex phase diagram akin to other strongly correlated materials. In this talk, I will provide a brief introduction to the rich and diverse field of moiré superlattices built by stacking and twisting graphene and other van der Waals materials. I will further present recent and ongoing projects – involving a combination of analytics, numerics, machine-learning, and experiment – which explore the exotic quantum many-body phases that can be stabilized in these platforms.

Twisted bilayer graphene (TBG) near the "magic angles" has emerged as a rich platform for strongly correlated states of two-dimensional (2D) Dirac semimetals. Topological insulator thin films because of their ability to host low energy Dirac nodes, presents another platform where ​"twistronics" can be used to engineer flat bands. However, topological insulator systems encounter some theoretical difficulties in engineering flat bands using the twistronics approach. I will discuss these issues. Using simple surface state electronic models for thin film magnetic topological insulators, I will show how flat moire bands can still be achieved in these systems. I will discuss the similarity and differences of such moire systems with the twisted multilayers of graphene and more recent developments in twisted multilayers of cuprate superconductors. Finally, I will discuss possible many body phases that can appear in these moire systems.

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.

I will present several approaches to the study of thermal Hall transport in quantum materials (esp. quantum magnets) when the main thermal Hall contribution is due to the transport of phonons coupled with electronic degrees of freedom.

Moiré heterostructures of transition metal dichalcogenides (TMD) have been shown to give rise to correlated insulating states at fractional fillings, forming self-organized charge lattices. The combination of spin-orbit coupling and moiré modulation can lead pseudomagnetic fields and associated fluxes patterns for electrons. We explore the possibility of spin-liquid states in these systems. We further discuss the effects of doping these correlated insulating states at fractional fillings.

We present a novel proposal for potential ground states of the $S=1/2$ and $S=1$ Heisenberg antiferromagnet on the pyrochlore lattice. The ground-state candidates form a simple family that is exponentially numerous in the linear size of the system. They can be visualized as coverings of hard hexagons, with each hexagon representing a resonating valence-bond ring, breaking various lattice symmetries such as rotation, inversion, and translation. By evaluating a simple variational wavefunction based on a single hard-hexagon covering, we achieve a precise variational energy consistent with density matrix renormalization group predictions and a numerical linked cluster expansion technique carried out at zero temperature. The scenario of a hard-hexagon state is backed up by carefully examining excitations on top of the valence-bond crystal as it provides further evidence of its stability. Our findings have broader implications as they extend to other frustrated magnets, such as the two-dimensional ruby and checkerboard lattices. In total, our work offers a new perspective, where the frustration effectively decouples unfrustrated motifs -- the hard hexagons in the pyrochlore lattice -- in quantum magnets. [1] Robin Schäfer, Benedikt Placke, Owen Benton, Roderich Moessner, arXiv:2210.07235

The variational cluster approach (VCA) belongs to one of the most successful self-energy-functional methods in treating many-body electron systems. In my talk, I will discuss its hybrid quantum-to-classical alternative. The latter uses digital quantum circuits to simulate a dynamics of many-electron systems via the Trotterization scheme and eventually to reconstruct the Green's function of a cluster in a polynomial time. I will outline a new quantum algorithm which uses an analog of the Kubo linear response theory adapted to quantum circuits which finds time-resolved correlation functions and the fermionic single-particle Green's function in particular. This new algorithm allows to circumvents the usage of a hardware demanding phase estimation scheme proposed in all previous works. I will demonstrate its performance for small size clusters on commercially available IMB transmon chips and finally elaborate on how far one may go with near-term quantum devices in revealing phase diagrams of 2D Fermi-Hubbard model. Work in collaboration with Gino Bishop and Frank K. Wilhelm.

A precise characterization of the recently discovered crossover to hydrodynamic transport in electron liquids, and in particular of a conjectured exotic odd-parity transport regime, requires a full solution of the Fermi-liquid collision integral at all temperatures beyond state-of-the-art analytic leading-logarithmic approximations. I will describe how to develop a general basis expansion of the linearized collision integral applicable at all temperatures, and employ this to determine the decay rates of Fermi surface perturbations in two-dimensional electron liquids. I will present evidence for a new odd-parity transport regime, in which parity-even Fermi surface deformations decay rapidly but odd-parity modes are anomalously long-lived, and which exists at fairly large temperatures $T \lesssim 0.1 T_F$, putting this regime within the reach of current experiments.

One of the fundamental questions in quantum many-body physics is whether its low-energy physics can be described in terms of quasiparticles -- or we are just left with the “unparticle” physics [1]. However, models with vanishing quasiparticles are often relatively complex and unrealistic. In fact, experiments on real materials usually suggest stable quasiparticle solutions. Here I will show that quasiparticles may be destroyed once fermions are coupled to a "large" number of zero-energy bosons [2]. Such a paradigm enables us to obtain an alternative explanation of the fractionalisation of electrons introduced into the 1D antiferromagnets [3]. Moreover, we identify two experimentally relevant cases which show a destruction of quasiparticles [3]. [1] J. Zaanen, SciPost Phys. 6, 061 (2019). [2] P. Wrzosek et al., Phys. Rev. B 107, 205103 (2023). [3] P. Wrzosek et al., arXiv:2203.01846 (under review); K. Wohlfeld, E. Demler, T. Tohyama, work in progress (2023).

It is known that the large-$q$ complex Sachdev–Ye–Kitaev (SYK) dot thermalizes instantaneously under rather general dynamical protocols. We consider a lattice of such dots coupled together, allowing for $r/2$ body hopping of particles between nearest neighbors. We develop a rather general analytical framework to study the dynamics to leading order in $1/q$ on such a lattice, allowing for arbitrary time dependent couplings, hence general dynamical protocols. We find that the physics of the diffusive case $r>2$ is effectively the same as the kinetic case $r=2$, assuming $r=\mathcal{O}(q^0)$. Remarkably, we find that the local charge densities $\mathcal{Q}_i$ form a closed set of equations. They however only show fluctuations of the order $\mathcal{O}(\mathcal{Q}_i/q)$, hence remaining constant in the limit $q\rightarrow \infty$. Despite this effective lack of charge dynamics, the dots do not in fact behave as isolated lattice sites which would thermalize instantaneously. Indeed, we show via a proof by contradiction that such instantaneously thermalize is not generally possible for a connected lattice. Importantly, the results are shown to be independent of the dimensionality of the lattice.

The locally noncentrosymmetric CeRh$_2$As$_2$ has recently rekindled interest in the physics of heavy fermion systems, with its complex phase diagram displaying two superconducting phases as a function of magnetic field. Curiously, the low-field pairing phase seems to coexist with antiferromagnetic order, that disappears at the internal phase transition. In this presentation I delve into some of the unresolved questions surrounding superconducting CeRh$_2$As$_2$, employing a phenomenological Ginzburg-Landau formalism. Closely guided by experimental results, our investigation primarily focuses on the coexistence of superconductivity and magnetism in the low-field phase, as well as the nature of the internal phase transition. To incorporate the magnetic order, we consider a doubled unit cell allowing for a comprehensive classification of order parameters under the pertinent nonsymmorphic space group. Within this context, I propose potential scenarios that elucidate the interplay between superconductivity and magnetism, as well as discuss possible experimental probes.