Winter School on Strongly Correlated Quantum Matter

We propose a scheme to create an electronic Floquet vortex state by irradiating the circularly-polarized laser light on the two-dimensional semiconductor. We study the properties of the Floquet vortex states analytically and numerically using methods analogous to the techniques used for the analysis of superconducting vortex states, while we exhibit that the Floquet vortex created in the current system has the wider tunability. To illustrate the impact of such tunability in quantum engineering, we demonstrate how this vortex state can be used for quantum information processing.

In this work we explore some of the capabilities of the multiconfiguration time-dependent Hartree approach (MCTDH), a general and powerful method to compute quantum dynamics simulations. Its strength lies in the particular ansatz it uses for the many-body wave function: a superposition, with time-dependent coefficients, of direct-product states which are built from a time-dependent one-particle basis. When one applies the time-dependent variational principle to this ansatz, a set of coupled equations is found for the coefficients and the one-particle basis functions. This ensures that, during a numerical solution of these equations, at every time the system is represented in a variationally optimal basis. We apply the MCTDH approach to a 1D system of soft bosons that undergoes a quantum phase transition from a standard Luttinger Liquid to a Cluster Luttinger Liquid (CLL). We simulate this system in real-time, and introduce a method for computing the energy of the low-lying excited states by observing the response of the system to a weak time-dependent periodic potential. In the Tonks-Girardeau condition, our results are in good accordance with the Bogolyubov spectrum.

Signatures of Many-Body Localization in the Dynamics of Two-Level Systems in Glasses Abstract: We investigate the quantum dynamics of two-level systems (TLSs) in glasses at low temperatures (1 K and below). We study an ensemble of TLSs coupled to phonons. By integrating out the phonons within the framework of the GKSL master equation, we derive the explicit form of the interactions among TLSs and of the dissipative terms. We find that the dynamics of the system shows clear signatures of many-body localization physics (in particular a power-law decay of the concurrence, which measures pairwise entanglement also in non-isolated systems) even in the presence of dissipation, if the latter is not too large. This feature can be ascribed to the presence of strong, long-tailed disorder characterizing the distributions of the model parameters. Our findings show that assuming ergodicity when discussing TLS physics might not be justified for all kinds of experiments on low-temperature glasses.

Signatures of Many-Body Localization in the Dynamics of Two-Level Systems in Glasses Abstract: We investigate the quantum dynamics of two-level systems (TLSs) in glasses at low temperatures (1 K and below). We study an ensemble of TLSs coupled to phonons. By integrating out the phonons within the framework of the GKSL master equation, we derive the explicit form of the interactions among TLSs and of the dissipative terms. We find that the dynamics of the system shows clear signatures of many-body localization physics (in particular a power-law decay of the concurrence, which measures pairwise entanglement also in non-isolated systems) even in the presence of dissipation, if the latter is not too large. This feature can be ascribed to the presence of strong, long-tailed disorder characterizing the distributions of the model parameters. Our findings show that assuming ergodicity when discussing TLS physics might not be justified for all kinds of experiments on low-temperature glasses.

We consider the relaxation properties of electron glass, which is a system in which all the electron states are localized and the dynamics occurs through phonon-assisted hopping amongst these states. We model the system by a lattice of localized states which have random energies and interact through the Coulomb interaction. The presence of disorder and the long-range interaction makes the system glassy which results in slow dynamics towards reaching equilibrium, aging (system dynamics depending on the history), and memory effects. Further, a much-discussed question is whether there is an equilibrium transition to glassy phase or not as the temperature is lowered. The wide range of timescales involved in such systems makes it more difficult to solve numerically. We have modeled the kinetics of site-occupation numbers as Ising spins by Kawasaki Dynamics (spin-exchange) as in our system only half the sites are occupied and the number of particles is conserved. The master equation governing the dynamics is solved in mean-field approximation. We use the eigenvalue distribution of the dynamical matrix to characterize relaxation laws as a function of localization length at low temperatures. Our results demonstrate the dominant role played by the localization length on the relaxation laws. For very small localization lengths we find a crossover from exponential relaxation at long times to a logarithmic decay at intermediate times. No logarithmic decay at the intermediate times is observed for large localization lengths.

The time evolution of the entanglement entropy is a key concept to understand the structure of a non-equilibrium quantum state. In a large class of models, such evolution can be understood in terms of a semiclassical picture of moving quasiparticles spreading the entanglement throughout the system. However, it is not yet known how the entanglement splits between the sectors of an internal local symmetry of a quantum many-body system. Here, guided by the examples of conformal field theories and free-fermion chains, we show that the quasiparticle picture can be adapted to this goal, leading to a general conjecture for the charged entropies whose Fourier transform gives the desired symmetry resolved entanglement $S_n(q)$. We point out two physically relevant effects that should be easily observed in atomic experiments: a delay time for the onset of $S_n(q)$ which grows linearly with $|\Delta q|$ (the difference from the charge $q$ and its mean value), and an effective equipartition when $|\Delta q|$ is much smaller than the subsystem size.

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

"The quantized Hall conductivity of integer and fractional quantum Hall (IQH and FQH) states is directly related to a topological invariant, the many-body Chern number. The conventional calculation of this invariant in interacting systems requires a family of many-body wave functions parameterized by twist angles in order to calculate the Berry curvature. In this work, we demonstrate how to extract the Chern number given a single many-body wave function, without knowledge of the Hamiltonian. We perform extensive numerical simulations involving IQH and FQH states to validate these methods. We also propose an ancilla-free experimental scheme for the measurement of this invariant. Specifically, we use the statistical correlations of randomized measurements to infer the MBCN of a wavefunction."

Quantum many-body scars represent a weak form of ergodicity breaking that gives rise to robust periodic revivals in kinetically constrained quantum systems, such as the PXP model describing strongly-interacting Rydberg atoms. By analogy to quantum scars in single-particle quantum billiards, the many-body scarred eigenstates are distinguished by their anomalous overlap with the so-called quasimodes, i.e., the wave functions that concentrate along classical periodic orbits. While the classical orbits in the PXP model have previously been constructed using the Time-Dependent Variational Principle (TDVP), the corresponding quasimodes have only been found numerically. Here we introduce a new approach to constructing quasimodes in the PXP model based on the subspace symmetrised over permutations on each sublattice. We show that this method is amenable to analytic treatment and leads to an efficient construction of the quasimodes, allowing to study the dynamics of the PXP model in large systems on the order of hundreds of atoms. Finally, our approach provides a tractable way of introducing quantum fluctuations at all orders on top of the classical equations of motion defined by the TDVP.

LiHoF4 is a quantum magnet known to be a good physical realization of the transverse field Ising model with dipolar interactions. Results from previous studies, using various Monte Carlo techniques and mean-field analyses, show a persistent discrepancy with experimental results for the $B_x − T$ phase diagram. Namely, in the low $B_x$ regime, the experimental phase boundary separating the ferromagnetic and paramagnetic phases has a much smaller dependence on magnetic field in comparison to the theoretical predictions. In this work we propose a mechanism which may account for the discrepancy. Offdiagonal terms of the dipolar interaction, more dominant in the disordered paramagnetic phase, reduce the energy of the paramagnetic phase, and consequently reduce the critical temperature. Using classical Monte Carlo simulations, in which we explicitly take the modification of the Ising states due to the offdiagonal terms into account, we show that the inclusion of the these terms reduces $T_c$ markedly at zero transverse field. We also show that the effect is diminished with increasing transverse field, leading to the above mentioned field dependence of the critical temperature.

We discuss a simple and experimentally available realization of fracton physics. We note that superfluid vortices conserve total dipole moment and trace of the quadrupole moment of vorticity. This establishes a relation to a traceless scalar charge theory in two spatial dimensions. We also consider the limit where the number of vortices is large and show that emergent vortex hydrodynamics conserves these moments too. Finally, we compare the motion of vortices and of fractons on curved surfaces; and find that they agree. This opens a route to experimental study of the interplay between fracton physics and curved space. Our conclusions also apply to charged particles in strong magnetic field. (Reference : D Doshi, A Gromov - arXiv preprint arXiv:2005.03015, 2020)

The presence of global conserved quantities in interacting systems generically leads to diffusive transport at late times. Here, we show that systems conserving the dipole moment of an associated global charge, or even higher moment generalizations thereof, escape this scenario, displaying subdiffusive decay instead. Modelling the time evolution as cellular automata for specific cases of dipole- and quadrupole-conservation, we numerically find distinct anomalous exponents of the late time relaxation. We explain these findings by analytically constructing a general hydrodynamic model that results in a series of exponents depending on the number of conserved moments, yielding an accurate description of the scaling form of charge correlation functions. We analyze the spatial profile of the correlations and discuss potential experimentally relevant signatures of higher moment conservation.

We study the localization properties of electrons in incommensurate twisted bilayer graphene for small angles, encompassing the narrow-band regime, by numerically exact means. Sub-ballistic states are found within the narrow-band region around the magic angle. Such states are delocalized in momentum-space and follow non-Poissonian level statistics, in contrast with their ballistic counterparts found for close commensurate angles. Transport results corroborate this picture: for large enough systems, the conductance decreases with system size for incommensurate angles within the sub-ballistic regime. Our results show that incommensurability effects are of crucial importance in the narrow-band regime. The incommensurate nature of a general twist angle must therefore be taken into account for an accurate description of magic-angle twisted bilayer graphene.

Recent experiments on Rydberg atom arrays have found evidence of anomalously slow thermalization and persistent density oscillations, which have been interpreted as a many-body analog of the phenomenon of quantum scars. Periodic dynamics and atypical scarred eigenstates originate from a "hard" kinetic constraint: the neighboring Rydberg atoms cannot be simultaneously excited. Here we propose a realization of quantum many-body scars in a 1D bosonic lattice model with a "soft" constraint in the form of density-assisted hopping. We discuss the relation of this model to the standard Bose-Hubbard model and possible experimental realizations using ultracold atoms. We find that this model exhibits similar phenomenology to the Rydberg atom chain, including weakly entangled eigenstates at high energy densities and the presence of a large number of exact zero energy states, with distinct algebraic structure.

While the physics of the edges between topological orders and vacuum has been thoroughly investigated, less is known about the properties of interfaces between different topological orders. Such systems have recently attracted significant attention, partly due to their potential applications in quantum computing. However, they are difficult to study numerically in a bottom-up manner, because relatively large system sizes are needed to capture their properties correctly. In this work, we overcome this obstacle by employing the conformal field theory to create model wavefunctions for interfaces between two different Laughlin states on the lattice. These objects can be studied using Monte Carlo methods for systems much larger than available within the exact diagonalization approach. We study their properties such as the entanglement entropy scaling and the correlation functions. Similar wavefunctions are also created for systems with localized anyons, allowing to extract the charge, the density profile and the mutual statistics of these excitations. Within our approach, we can explicitly simulate the crossing of the interface by the anyons and show that some of them lose their fractional statistics in such a process, which is in accordance with earlier “top-down” results obtained from field theory, and is possibly related to the entanglement entropy scaling at the interface.

Gauge pumps are spatially-resolved probes that can reveal discrete symmetries due to nontrivial topology. We introduce the Floquet gauge pump whereby a dynamically engineered Floquet Hamiltonian is employed to reveal the inherent topology of the ground state in interacting systems. We demonstrate this concept in a 1D XY model with periodically driven couplings and a transverse field. In the high-frequency limit, we obtain a Floquet Hamiltonian consisting of the static XY and dynamically generated Dzyaloshinsky-Moriya interactions (DMI) terms. We show that anisotropy in the couplings facilitates a magnetization current across a dynamically imprinted junction. In fermionic language, this corresponds to an unconventional Josephson junction with both hopping and pairing tunneling terms. The magnetization current depends on the phases of complex coupling terms, with the XY interaction as the real and DMI as the imaginary part. It shows 4π periodicity revealing the topological nature of the ground state manifold in the ordered phase, in contrast to the trivial topology in the disordered phase. We discuss the requirements to realize the Floquet gauge pump with interacting trapped ions.

We explore the relaxation dynamics of elementary spin clusters of a kinetically constrained spin system. Inspired by experiments with Rydberg lattice gases, we focus on the situation in which an excited spin leads to a "facilitated" excitation of a neighboring spin. We show that even weak interactions that extend beyond nearest neighbors can have a dramatic impact on the relaxation behavior: they generate a linear potential, which under certain conditions leads to the onset of Bloch oscillations of spin clusters. These hinder the expansion of a cluster and more generally the relaxation of many-body states towards equilibrium. This shows that non-ergodic behavior in kinetically constrained systems may occur as a consequence of the interplay between reduced connectivity of many-body states and weak interparticle interactions. We furthermore show that the emergent Bloch oscillations identified here can be detected in experiment through measurements of the Rydberg atom density, and discuss how spin-orbit coupling between internal and external degrees of freedom of spin clusters can be used to control their relaxation behavior.

Recently, there has been much interest in the efficient preparation of complex quantum states using low-depth quantum circuits, such as Quantum Approximate Optimization Algorithm (QAOA). While it has been numerically shown that such algorithms prepare certain correlated states of quantum spins with surprising accuracy, a systematic way of quantifying the efficiency of QAOA in general classes of models has been lacking. Here, we propose that the success of QAOA in preparing ordered states is related to the interaction distance of the target state, which measures how close that state is to the manifold of all Gaussian states in an arbitrary basis of single-particle modes. We numerically verify this for the ground state of the quantum Ising model with arbitrary transverse and longitudinal field strengths, a canonical example of a non-integrable model. Our results suggest that the structure of the entanglement spectrum, as witnessed by the interaction distance, correlates with the success of QAOA state preparation. We conclude that QAOA typically finds a solution that perturbs around the closest free-fermion state.

Nanoelectronics devices such as semiconductor quantum dots and single molecule transistors exhibit a rich range of physical behavior due to the interplay between orbital complexity, strong electronic correlations and device geometry. Understanding and simulating the quantum transport through such nanostructures is essential for rational design and technological applications. In this poster, I present theoretical reformulations electrical conductance formulae for interacting mesoscopic quantum transport calculations in linear response, and demonstrate the improvement over standard methods with several example applications using the numerical renormalization group technique. I will treat reformulations of the Meir-Wingreen formula in the context of non-proportionate coupling set-ups and by means of perturbative verification of the Ng ansatz; of the Oguri formula in non-Fermi Liquid states and of the Kubo formula for conductance.

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

We study the spin-$1/2$ ferromagnetic Heisenberg-Kitaev-$\Gamma$ model in the anisotropic (Toric code) limit to reveal the nature of the quantum phase transition between the gapped $Z_2$ quantum spin liquid and a spin ordered phase (driven by Heisenberg interactions) as well as a trivial paramagnet (driven by pseudo-dipolar interactions, $\Gamma$). The transitions are obtained by a simultaneous condensation of the Ising electric and magnetic charges-- the fractionalized excitations of the $Z_2$ quantum spin liquid. Both these transitions can be continuous and are examples of deconfined quantum critical points. Crucial to our calculations are the symmetry implementations on the soft electric and magnetic modes that become critical. In particular, we find strong constraints on the structure of the critical theory arising from time reversal and lattice translation symmetries with the latter acting as an anyon permutation symmetry that endows the critical theory with a manifestly self-dual structure. We find that the transition between the quantum spin liquid and the spin-ordered phase belongs to a self-dual modified Abelian Higgs field theory while that between the spin liquid and the trivial paramagnet belongs to a self-dual $Z_2$ gauge theory. We also study the effect of an external Zeeman field to show an interesting similarity between the polarised paramagnet obtained due to the Zeeman field and the trivial paramagnet driven the pseudo-dipolar interactions. Interestingly, both the spin liquid and the spin ordered phases have easily identifiable counterparts in the isotropic limit and the present calculations may shed insights into the corresponding transitions in the material relevant isotropic limit.

In this work, the capability of restricted Boltzmann machines (RBMs) to find solutions for the Kitaev honeycomb model is investigated. The measured groundstate (GS) energy of the system is compared and shown to reside within a few percent error of the analytically derived value of the energy per plaquette. Moreover, given a set of single shot measurements of exact solutions of the model, an RBM is used to perform quantum state tomography and the obtained result has a $97\%$ overlap with the exact analytic result. Furthermore, the possibility of realizing anyons in the RBM is discussed and an algorithm is given to build these anyonic excitations and braid them as a proof of concept for performing quantum gates and doing quantum computation.

Interacting systems of Rydberg atoms have attracted much attention recently, partly due to their strong interactions and high stability. Furthermore, experimental techniques have been proposed to include synthetic gauge fields and correlated hopping, where the excitation transport between two atoms depends on the quantum state of a third atom. In our work, we are considering a system of Rydberg atoms on a two-dimensional hexagonal lattice, including both synthetic gauge fields and correlated hopping. We numerically obtain a rich phase diagram,including two disordered regimes where we find evidence to support the existence of a chiral spin-liquid-state.

Studying the out-of-equilibrium quantum dynamics in two-dimensional lattice models is challenging due to the lack of a general purpose simulation method. A new semiclassical approach to compute the quantum dynamics of fermions was recently developed by Davidson et. al [1], the fermionic truncated Wigner approximation (fTWA). Here, we adopt the method and combine it with the limit of high fermion degeneracy $N$ as a well-defined semiclassical expansion parameter. On the poster we consider the well-known problem of an interaction quench in the two-dimensional Hubbard model to show that the method correctly describes prethermalization [2]. In addition we discuss whether the long-time thermalization dynamics is reproduced as well. As a second application we consider quenches in ordered phases of the large-$N$ Hubbard-Heisenberg model and show that the semiclassical time-evolution leads to dephasing and subsequent decay of the order parameter. [1] SM Davidson et. al., Annals of Physics 384, pages 128-141 (2017) [2] A Osterkorn and S Kehrein, arXiv:2007.05063

Oxide perovskites have received widespread attention ever since their discovery due to the multiple physical properties they exhibit, including ferroelectricity, multiferroicity, and superconductivity. One prominent absence in this list of properties that oxide perovskites exhibit is electronic topological order. This is a consequence of the large band gaps of oxide perovskites, which make the band inversions necessary for topology impossible. We find that topological phonons – nodal rings, nodal lines, and Weyl points – are ubiquitous in oxide perovskites in terms of structures (tetragonal, orthorhombic, and rhombohedral), compounds (BaTiO$_3$, PbTiO$_3$, and SrTiO$_3$), and external conditions (photoexcitation, strain, and temperature). In particular, in the tetragonal phase of these compounds all types of topological phonons can simultaneously emerge when stabilized by photoexcitation, whereas the tetragonal phase stabilized by thermal fluctuations only hosts a more limited set of topological phonon states. In addition, we find that the photoexcited carrier density can be used to control the emergent topological states, for example driving the creation/annihilation of Weyl points and switching between nodal lines and nodal rings. Overall, we propose oxide perovskites as a versatile platform in which to study topological phonons and their manipulation with light [1]. Reference: [1] Bo Peng, Yuchen Hu, Shuichi Murakami, Tiantian Zhang, Bartomeu Monserrat. Topological phonons in oxide perovskites controlled by light. Science Advances 6, eabd1618 (2020).

Discrete time crystals are periodically driven systems characterized by a response with periodicity $nT$, with $T$ the period of the drive and $n>1$. Typically, $n$ is an integer and bounded from above by the dimension of the local (or single particle) Hilbert space, the most prominent example being spin-$1/2$ systems with $n$ restricted to $2$. Here we show that a clean spin-$1/2$ system in the presence of long-range interactions and transverse field can sustain a huge variety of different `higher-order' discrete time crystals with integer and, surprisingly, even fractional $n > 2$. We characterize these (arguably prethermal) non-equilibrium phases of matter thoroughly using a combination of exact diagonalization, semiclassical methods, and spin-wave approximations, which enable us to establish their stability in the presence of competing long- and short-range interactions. Remarkably, these phases emerge in a model with continous driving and time-independent interactions, convenient for experimental implementations with ultracold atoms or trapped ions.

We study in detail the properties of pi-fluxes embedded in a state with a finite density of anyons that form either a Fermi liquid or a Bose-Einstein condensate. By employing a recently developed exact lattice bosonization in 2D, we demonstrate that such pi-flux remains a fully deconfined quasiparticle with a finite energy cost in a Fermi liquid of emergent fermions coupled to a Z2 gauge field. This pi-flux is accompanied by a screening cloud of fermions, which in the case of a Fermi gas with a parabolic dispersion binds exactly 1/8 of a fermionic hole. In addition there is a long-ranged power-law oscillatory disturbance of the liquid surrounding the pi-flux akin to Friedel oscillations. These results carry over directly to the pi-flux excitations in orthogonal metals. In sharp contrast, when the pi-flux is surrounded by a Bose-Einstein condensate of particles coupled to a Z2 gauge field, it binds a superfluid half-vortex, becoming a marginally confined excitation with a logarithmic energy cost divergence.

It has recently been predicted that many-body localization survives the presence of coupling to a non-local degree of freedom, such as a cavity mode [PRL 122, 240402 (2019)]. This poster presents recent results on anomalous properties of localization in such a setup. First, we show that in a central qudit model, an inverted mobility edge occurs, meaning that infinite temperature states are localized while low energy states are delocalized. This model may be directly realized by extending recent work on artificial cavities using atom-like mirrors [Nature 569.7758: 692 (2019)]; similar results hold for central spin models or cavity QED with appropriate cavity non-linearity. Second, we suggest a platform for realizing time crystals in cavity QED and in the absence of drive.

An important milestone towards “quantum supremacy” has been recently achieved by using Google’s noisy intermediate-scale quantum (NISQ) device Sycamore to sample from the output distribution of (pseudo-)random circuits involving up to 53 qubits. We argue that such random circuits provide tailor-made building blocks for the simulation of quantum many-body systems on NISQ devices. Specifically, we propose a two-part algorithm consisting of a random circuit followed by a trotterized Hamiltonian time evolution, which we numerically exemplify by studying the buildup of spatiotemporal correlations in one- and two-dimensional quantum spin systems. Importantly, we find that the emerging hydrodynamic scaling of the correlations is highly robust with respect to the size of the Trotter step, opening the door to reach nontrivial time scales with a small number of elementary gates. While errors within the random circuit are shown to be irrelevant for our approach, we furthermore unveil that meaningful results can be obtained for noisy time evolutions with error rates achievable on near-term hardware.

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

Scattering processes are a crucial ingredient for the investigation of the fundamental interactions. Working in the framework of Hamiltonian lattice quantum field theory, we attack this problem via numerical tensor network simulations. We focus on the theory of quantum electrodynamics in $1+1$ spacetime dimensions but develop a set of tools which are relevant for a broader class of $1+1$ dimensional quantum field theories. Specifically, we identify a matrix product state representation of the initial momentum wave packet and compute its real-time dynamics. The outcome of some scattering simulations is presented.

We use large-scale exact diagonalization to study the quantum Ising chain in a transverse field with long-range power-law interactions decaying with exponent $\alpha$. Analyzing various eigenstate and eigenvalue properties, we find numerical evidence for ergodic behavior in the thermodynamic limit for $\alpha>0$, i.e. for the slightest breaking of the permutation symmetry at $\alpha=0$. Considering an excited-states fidelity susceptibility, an energy-resolved average level-spacing ratio and the eigenstate expectations of observables, we observe that a behavior consistent with eigenstate thermalization first emerges at high energy densities for finite system sizes, as soon as $\alpha>0$. We argue that ergodicity moves towards lower energy densities for increasing system sizes. While we argue the system to be ergodic for any $\alpha>0$, we also find a peculiar behaviour near $\alpha=2$ suggesting the proximity to a yet unknown integrable point. We further study the symmetry-breaking properties of the eigenstates. We argue that for weak transverse fields the eigenstates break the $\mathbb{Z}_2$ symmetry, and show long-range order, at finite excitation energy densities for all the values of $\alpha$ we can technically address ($\alpha\leq 1.5$). Our contribution settles central theoretical questions on long-range quantum Ising chains and are also interesting for the nonequilibrium dynamics of trapped ions.

We use a combination of three computational methods to investigate the notoriously difficult frustrated three-dimensional pyrochlore S=12 quantum antiferromagnet, at finite temperature T: canonical typicality for a finite cluster of 2×2×2 unit cells (i.e., 32 sites), a finite-T matrix product state method on a larger cluster with 48 sites, and the numerical linked cluster expansion (NLCE) using clusters up to 25 lattice sites, including nontrivial hexagonal and octagonal loops. We calculate thermodynamic properties (energy, specific heat capacity, entropy, susceptibility, magnetization) and the static structure factor. We find a pronounced maximum in the specific heat at $T=0.57J$, which is stable across finite size clusters and converged in the series expansion. At $T\approx 0.25J$ (the limit of convergence of our method), the residual entropy per spin is $0.47k_B\log(2)$, which is relatively large compared to other frustrated models at this temperature. We also observe a nonmonotonic dependence on T of the magnetization at low magnetic fields, reflecting the dominantly nonmagnetic character of the low-energy states. A detailed comparison of our results to measurements for the $S=1$ material $NaCaNi_2F_7$ yields a rough agreement of the functional form of the specific heat maximum, which in turn differs from the sharper maximum of the heat capacity of the spin ice material $Dy_2Ti_2O_7$.

Simulating real-time evolution in theories of fundamental interactions represents one of the central challenges in contemporary theoretical physics. Cold-atom platforms represent promising candidates to realize quantum simulations of non-perturbative phenomena in gauge theories, such as vacuum decay and hadron collisions, in extreme conditions prohibitive for direct experiments. In this work, we demonstrate that present-day quantum simulators can give access to S-matrix measurements of elastic and inelastic meson collisions in Abelian gauge theories, mimicking experiments with linear particle accelerators. Considering for definiteness a $(1 + 1)$-dimensional $\mathbb{Z}_2$-lattice gauge theory realizable with Rydberg-atom arrays, we solve the meson scattering problem exactly in the limit of large fermion mass and for arbitrary coupling strength.

Neural quantum states are a promising approach to study many-body quantum physics. However, they face a major challenge when applied to lattice models: Neural networks struggle to converge to ground states with a nontrivial sign structure. In this talk, I present a neural network architecture with a simple, explicit, and interpretable phase ansatz, which can robustly represent such states and achieve state-of-the-art variational energies for both conventional and frustrated antiferromagnets. In the first case, the neural network correctly recovers the Marshall sign rule without any prior knowledge. For frustrated magnets, our approach uncovers low-energy states that exhibit the Marshall sign rule but does not reach the true ground state, which is expected to have a different sign structure. I discuss the possible origins of this "residual sign problem" as well as strategies for overcoming it, which may allow using neural quantum states for challenging spin liquid problems.

System-environment interactions have been studied extensively for many decades and recent developments in quantum optics and circuit QED provide intriguing possibilities for realizing non-linear environments. The Bose-Hubbard lattice for photons, e.g., has been realized experimentally using superconducting circuits, thereby providing an exciting platform to study effective interactions between quantum emitters mediated by the engineered photonic environment. We consider a collection of macroscopically separated two-level emitters coupled to a non-linear environment and study the dissipative dynamics. Specifically, we report our theoretical progress on understanding the criteria for the existence of specific emission pathways as a function of the positions of the emitters.

We present an algorithm for studying quantum systems at finite temperature using continuous matrix product operator representation. The approach handles both short-range and long-range interactions in the thermodynamic limit without incurring any time discretization error. Moreover, the approach provides direct access to physical observables including the specific heat, local susceptibility, and local spectral functions. After verifying the method using the prototypical quantum XXZ chains, we apply it to quantum Ising models with power-law decaying interactions and on the infinite cylinder, respectively. The approach offers predictions that are relevant to experiments in quantum simulators and the nuclear magnetic resonance spin-lattice relaxation rate.

We investigate the finite temperature dynamics of the sine-Gordon model by studying its dynamical correlation functions at low temperatures in the semiclassical approach. Going beyond previous analyses based on perfectly reflective or transmissive collision dynamics of the gapped solitonic excitations, we focus on the generic case when both transmissive and reflective scatterings are present. We argue that the behaviour of the correlation functions is qualitatively different from both special cases, in particular, the autocorrelation function decays in time neither exponentially nor as a power-law, but assumes a squeezed exponential form. Supporting our claim, we perform numerical simulations utilizing the exact S-matrix of the model.

In this work we consider two-dimensional, non-centrosymmetric antiferromagnets, for which the competition between exchange and Dyzaloshinskii-Moriya interaction leads to the formation of spatially modulated phases of the staggered order parameter. Within the framework of Ginzburg-Landau theory we show that by applying a magnetic field parallel to the c-axis, which thus induces easy-plane anisotropy, one can stabilize a square lattice of vortices close to Neel temperature. Upon decreasing temperature, this vortex phase undergoes spontaneous symmetry breaking into a rectangular phase, which was not anticipated before. We discuss the relevance of our results for the chiral antiferromagnet Ba2CuGe2O7.

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

Motivated by water, we proposed a lattice liquid model of dipolar dimers. We show that on bipartite lattice it can be exactly mapped to annealed Ising models on random graphs. With exactly solved Ising models, we cannot only prove the existence of the liquid-liquid phase transition, but also bound the critical temperature tightly around $k_BT_c = 3.5J$ , which is also confirmed by Monte Carlo simulation.

We study heating in interacting quantum many-body systems driven by random sequences with $n-$multipolar correlations, corresponding to a polynomially suppressed low frequency spectrum. For $n\geq1$, we find a prethermal regime, the lifetime of which grows algebraically with the driving rate, with exponent ${2n+1}$. A simple theory based on Fermi's golden rule accounts for this behaviour. The quasiperiodic Thue-Morse sequence corresponds to the $n\to \infty$ limit, and accordingly exhibits an exponentially long-lived prethermal regime. Despite the absence of periodicity in the drive, and in spite of its eventual heat death, the prethermal regime can host versatile non-equilibrium phases, which we illustrate with a random multipolar discrete time crystal.

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