Thermalization in quantum many-body systems is a central problem of quantum mechanics. Despite the unitary nature of quantum evolution, isolated many-body systems often appear to relax toward states that are locally described by statistical ensembles. However, phenomena such as integrability and quantum many-body scars demonstrate that thermalization is not universal and can fail in unexpected ways, leading to nonergodic dynamics and long-lived nonequilibrium behavior. In this thesis, the problem is addressed from multiple complementary perspectives, including thermalization, integrability breaking, constrained dynamics, and quantum many-body scars, together with the development of new tensor-network methods for nonequilibrium quantum systems and quantum metrological applications. First, we study energy-filtering protocols for the preparation of thermal states, analyzing the possibility of simulating them classically through the behavior of entanglement and correlations. The effects of weak integrability breaking are then investigated in models relevant to Rydberg-atom experiments, leading to the identification of novel scattering mechanisms and the introduction of subsystem variance as a sensitive probe of weak integrability breaking. A part of the thesis is devoted to quantum many-body scars and their consequences for relaxation and transport phenomena. Their dynamical signatures are studied in both closed and open quantum systems, revealing new mechanisms that sustain long-lived nonequilibrium behavior. The thermalization processes arising during the quasi-adiabatic preparation of the ground state in the trapped Bose-Hubbard model are also examined, showing how transport constraints can stabilize low-entropy states under experimentally realistic conditions. Finally, a novel tensor-network approach based on Tree Tensor Operators is introduced for the efficient computation of the Quantum Fisher Information of generic mixed states. Applicable to both closed and open quantum systems, the method provides a promising numerical tool for quantum sensing and metrological applications.
Thermalization in quantum many-body systems is a central problem of quantum mechanics. Despite the unitary nature of quantum evolution, isolated many-body systems often appear to relax toward states that are locally described by statistical ensembles. However, phenomena such as integrability and quantum many-body scars demonstrate that thermalization is not universal and can fail in unexpected ways, leading to nonergodic dynamics and long-lived nonequilibrium behavior. In this thesis, the problem is addressed from multiple complementary perspectives, including thermalization, integrability breaking, constrained dynamics, and quantum many-body scars, together with the development of new tensor-network methods for nonequilibrium quantum systems and quantum metrological applications. First, we study energy-filtering protocols for the preparation of thermal states, analyzing the possibility of simulating them classically through the behavior of entanglement and correlations. The effects of weak integrability breaking are then investigated in models relevant to Rydberg-atom experiments, leading to the identification of novel scattering mechanisms and the introduction of subsystem variance as a sensitive probe of weak integrability breaking. A part of the thesis is devoted to quantum many-body scars and their consequences for relaxation and transport phenomena. Their dynamical signatures are studied in both closed and open quantum systems, revealing new mechanisms that sustain long-lived nonequilibrium behavior. The thermalization processes arising during the quasi-adiabatic preparation of the ground state in the trapped Bose-Hubbard model are also examined, showing how transport constraints can stabilize low-entropy states under experimentally realistic conditions. Finally, a novel tensor-network approach based on Tree Tensor Operators is introduced for the efficient computation of the Quantum Fisher Information of generic mixed states. Applicable to both closed and open quantum systems, the method provides a promising numerical tool for quantum sensing and metrological applications.
This thesis investigates the anomalous dynamics observed in a Rydberg atom experiment in the broadest sense: a strongly interacting spin chain, without integrability or disorder, exhibits coherent many-body revivals ensuing only from specific initial states. This non-thermal behavior is attributed to the presence of quantum many-body scars (QMBS), a novel class of ergodicity breaking phenomena. Unlike other non-thermalizing systems such as integrable models and many-body localization, the mechanism of ergodicity breaking in QMBS is quite subtle, relying on a (vanishingly) small subset of anomalous eigenstates, known as scar states: one could observe ergodicity breaking only if initial states have appreciable overlap with these scar states. In other words, systems hosting QMBS are indistinguishable from typical chaotic, thermalizing systems, except for scar states. While the theoretical understanding of QMBS has advanced through the investigation of various toy quantum models, ranging from the Affleck-Kennedy-Lieb-Tasaki (AKLT) model to the Hubbard model, these insights do not fully resolve the mysterious oscillations in the Rydberg experiment: crucially the wavefunction corresponding to the experiment, and its relation to many other toy models in the literature remain open questions. Furthermore, beyond mathematical curiocity, the observability of non-thermal dynamics suggests that QMBS may yield distinct physical effects. the nature of which remains to be determined. This dissertation addresses these issues by solving two concrete problems: (i) the mathematical characterization of scar states in the PXP model, the effective model for the experiment, and (ii) the identification of physical consequences of QMBS in both short- and long-time dynamics. In the first part, we clarify the algebraic structure underlying the scar states of the PXP model and derive analytic ansatz for these wavefunctions. The proposed forms make explicit the hidden algebraic structure of the PXP scars and demonstrate how this structure is shared with many other QMBS Hamiltonians, including the AKLT model. The second part investigates dynamical signatures and robustness. Given the fragility of many-body eigenstates to perturbations, identifying which scar characteristics survive realistic perturbations is crucial. In closed systems, we show that out-of-time-ordered correlators (OTOCs) and the associated Lyapunov exponent can distinguish QMBS from generic chaotic states, at least within a semiclassical regime. Specifically, the OTOC growth associated with scar states is parametrically slower and remains slow under small ``scar-breaking'' perturbations. For open systems governed by non-Hermitian dynamics, we introduce a novel non-equilibrium phase, the QMBS phase, where the long-time wavefunction is localized in a small corner of the Hilbert space. We further identify a first-order transition between the QMBS phase and a thermal phase, where the wavefunction becomes delocalized.
Quantum chaos and the eigenstate thermalization hypothesis are based on the assumption of the validity of random matrix theory description on the spectrum and eigenstates. They provide the foundation and descriptions for the typical dynamics and thermalization in generic closed quantum systems. In this thesis, we investigate situations where the systems show atypical dynamics or anomalous thermalization, conflicting with the usual expectations from quantum chaos and eigenstate thermalization hypothesis. We first examine weak thermalization in a nonintegrable spin chain. The system shows long-lived strong oscillations and relaxes to the thermal equilibrium weakly. We identify the dynamics describable by quasiparticles and recognize the oscillation frequency to be the quasiparticle mass gap. We also estimate the damping time for the oscillations. Next, we study prethermalization, a phenomenon where a system relaxes to an intermediate almost-equilibrium stage before reaching the true thermal equilibrium. We study a nonintegrable spin chain in the strong coupling limit, where an almost-conserved quantity emerges and gives rise to the prethermalization. We also study a newly proposed diagnostic for quantum chaos: out-of-time-ordered correlators. Contrasting to the chaotic systems, we inspect their behaviors in various noninteracting integrable models. Finally, we dig into the quantum many-body scar states in the PXP model which describes a Rydberg atom chain. These special states do not satisfy the random matrix theory description nor the eigenstate thermalization hypothesis, therefore defying quantum chaos.
This thesis addresses different aspects of the dynamics of isolated quantum many-body systems far from equilibrium, ranging from transient phenomena at short times to questions about relaxation and equilibration at late times. The first part deals with nonequilibrium critical phenomena. Dynamical quantum phase transitions are characterized in a two-dimensional spin system by studying the distribution of Fisher zeros in the complex time plane. Moreover, a new topologically driven transition in the nonequilibrium steady state of quenched Chern insulators is investigated, resulting in the identification of universal nonanalytic behavior of the Hall conductance as a function of the quench parameter. The second part of the thesis comprises a study of transient dynamics of the transverse-field Ising model in two and three dimensions based on a perturbative derivation of classical networks to encode the time-evolved wave function; this construction is also applicable to represent the state as an artificial neural network. In the last part of the thesis a possible definition of the irreversibility of quantum many-body dynamics is introduced, which is based on the echo dynamics of observables under imperfect effective time reversal. Echo dynamics is studied in generic and integrable quantum systems as well as in the semiclassical limit. The relation to out-of-time-order correlators is explored, which were recently introduced to probe the quantum butterfly effect.
The experimental control and observation of quantum many-body systems has become a reality with the advent of ultracold quantum matter. The high level of isolation of these experiments, together with the development of novel measurement techniques, has revived a fundamental debate concerning the thermal equilibration of isolated quantum systems, commonly named "quantum thermalization". In this thesis we make use of a quantum-gas microscope to explore the thermalizing dynamics of highly isolated systems of ultracold bosonic atoms in optical lattices. The ability to prepare and control quantum systems made up of hundreds of atoms makes it possible to explore regimes that represent a challenge for classical numeric simulations. A major part of this dissertation deals with Bose-Hubbard systems in the presence of quenched disorder. We begin by studying the microscopic properties of its phases near equilibrium, where by tuning the strength of the disorder, observe features consistent with the emergence of a so-called Bose-glass phase. We then continue by preparing states far from equilibrium and exploring their quantum many-body dynamics. In particular, we observe signatures of the phenomenon of "many-body localization", which implies a breakdown of quantum thermalization. In addition, we study whether localized systems can be thermalized via the coupling to a bath of few degrees of freedom, i.e. a quantum bath. We do so by preparing a mixture of two interacting atomic species, where one acts as the bath and the other as the localized system. We do observe delocalizing dynamics for large enough baths, though in regimes of weak coupling localization can survive for extremely long times. The second main topic of this thesis is the thermalization of periodically driven many-body systems, so-called Floquet thermalization. In these systems, the absence of energy conservation eventually brings any initial state into a featureless infinite-temperature one. However, for sufficiently high frequencies this thermalization process can take arbitrarily long times, which can enable the engineering of exotic long-lived prethermal states. We use the high isolation of our system, together with the high sensitivity of quantum-gas microscopy, to measure the heating rates for a range of driving frequencies and interaction regimes. Our results show a dramatic suppression of the heating as the frequency of the drive is increased, which is consistent with theoretical expectations.
Understanding how quantum matter behaves when driven out of equilibrium is one of the key focuses in quantum physics. Thanks to impressive progress in the control and precision achieved in quantum synthetic matter over the past decades, the nonequilibrium quantum many-body physics has become one of the most active research areas today, especially after the experimental realization of Bose-Einstein condensates and optical lattices, which allows us to directly observe and study nonequilibrium quantum matter with great accuracy and controllability. In this dissertation, I explore the rich landscape of nonequilibrium quantum many-body physics and how quantum phase transitions, both symmetry-breaking and topological, can be extended to the nonequilibrium setting. In the first part of the dissertation, I focus on spinor Bose-Einstein condensates as an isolated quantum many-body system, and reveal their various dynamical behaviors, including quantum collapse and revivals, thermalization and nonthermal equilibration with no revival even though the system has finite degrees of freedom. In contrast to typical integrable systems, which usually do not thermalize, we find that spinor condensates have a parameter range in which the system thermalizes via the Eigenstate Thermalization Hypothesis (ETH). We show that this observation is linked to the presence of rare nonthermal states whose fraction vanishes with system size, and contributes to the notion of thermalization via weak ETH. Next, I explore a dynamical process that is complementary to thermalization in isolated quantum systems: information scrambling, which could be probed via out-of-time-order correlators (OTOC). I propose a nonintegrable, disordered and quasi-1D spin model, the ladder-XX model, for a feasible detection of information scrambling in a cold atom simulator. This chapter poses a fundamental question: "What are the signatures of quantum phases and phase transitions in isolated interacting systems driven out-of-equilibrium?" I study the ladder-XX model in both clean and disordered potentials, and characterize different nonequilibrium phases, i.e., ergodic and many-body localized, of the model based on the decay properties of OTOCs. Emergent light cone shows sublinear behavior, while the butterfly cones drastically differ from the light cone by demonstrating superlinear spread of information with a velocity that is bounded by the light cone velocity. In the second part of the dissertation, I continue to search for answers to the question posed above, however this time with a particular focus on symmetry-breaking and topological quantum phase transitions. I pin down a universal mechanism underlying the relation between information scrambling at any temperature and quantum phases at low temperatures. Our method points to key ingredients to dynamically detect long-range order in gapped phases through OTOCs for symmetry-breaking quantum phase transitions and Z2 topological order associated with Majorana zero modes localized at the edges. Our results pave the way to an intriguing observation that phases of quantum matter could protect the information from scrambling and thermalization, even when the system is interacting and nonintegrable. Finally, I explore and propose utilizing short-time transient temporal regimes and single-site probes to detect the phases and phase transitions in quantum matter. These studies reveal a dynamical crossover and a dynamical phase transition, respectively for periodic and open-boundary chains. In both cases, a nonequilibrium scaling law appears in the vicinity of the crossover/transition with associated exponents that differ from the analytical predictions for long times. Feasibility of detecting such dynamical criticality in experimental systems are discussed.
The ongoing quest for understanding nonequilibrium dynamics of complex quantum systems underpins the foundation of statistical physics as well as the development of quantum technology. Quantum many-body scarring has recently opened a window into novel mechanisms for delaying the onset of thermalization by preparing the system in special initial states, such as the Z2 state in a Rydberg atom system. Here we realize many-body scarring in a Bose-Hubbard quantum simulator from previously unknown initial conditions such as the unit-filling state. We develop a quantum-interference protocol for measuring the entanglement entropy and demonstrate that scarring traps the many-body system in a low-entropy subspace. Our work makes the resource of scarring accessible to a broad class of ultracold-atom experiments, and it allows one to explore the relation of scarring to constrained dynamics in lattice gauge theories, Hilbert space fragmentation, and disorder-free localization.