In this Thesis, we investigate problems of thermalization in closed (or isolated) and open quantum many-body systems, which are deeply tied to the foundations of quantum statistical mechanics.Such studies have attracted growing interest thanks to recent experimental realizations of controllable quantum many-body systems, e.g., cold atoms and ions.We firstly discuss thermalization in closed quantum many-body systems.The eigenstate thermalization hypothesis (ETH) has been proposed as a sufficient condition for a system to be described by the microcanonical ensemble after a long-time dynamics.The ETH is expected to hold true for generic systems except for some systems such as many-body localized (MBL) systems with strong disorder.On the other hand, the reason why the ETH generically holds truehas not yet been fully understood.We here rigorously show that the typicality argument, which has long been thought to justify the ETH, does not hold true for a realistic setup with few-body properties of observables and Hamiltonians.We secondly discuss thermalization in open quantum many-body systems.State-of-the-art experiments (e.g., experiments under continuous measurement) have now enabled us to control dissipation, which may enrich properties of closed systems.As one of the fundamental problems of thermalization in open quantum systems, we study the MBL in non-Hermitian systems, which are relevant for continuously measured systems.We show that the transition between delocalized (ETH) and MBL phases occurs even for non-Hermitian many-body Hamiltonians and affects spectral and dynamical properties.In particular, we find that a novel real-complex transition occurs upon MBL and affects the dynamical stability in non-Hermitian interacting systems with asymmetric hopping.Just as delocalized phases in closed systems are characterized by Hermitian random matrices, those in open quantum systems are characterized by non-Hermitian random matrices.On the other hand, in contrast with the Hermitian cases, the universality in non-Hermitian random matrices and its relation to symmetries are not well understood.In Hermitian random matrices, there are three universality classes of local spectral statistics dependent on time-reversal symmetry (TRS).However, TRS is known not to alter universality in non-Hermitian random matrices.We here show that three different universal level-spacing distributions appear even for non-Hermitian random matrices when we consider transposition symmetry instead of TRS.This result serves as a basis for characterizing nonintegrability and delocalization in open quantum systems with symmetry.asymmetric hopping . . . .
The recent discovery of persistent revivals in the Rydberg-atom quantum simulator has revealed a weakly ergodicity-breaking mechanism dubbed quantum many-body scars, which are a set of nonthermal states embedded in otherwise thermal spectra. Until now, such a mechanism has been mainly studied in Hermitian systems. Here, we establish the non-Hermitian quantum many-body scars and systematically characterize their nature from dynamic revivals, entanglement entropy, physical observables, and energy level statistics. Notably, we find the non-Hermitian quantum many-body scars exhibit significantly enhanced coherent revival dynamics when approaching the exceptional point. The signatures of non-Hermitian scars switch from the real-energy axis to the imaginary-energy axis after a real-to-complex spectrum transition driven by increasing non-Hermiticity, where an exceptional point and a quantum tricritical point emerge simultaneously. We further examine the stability of non-Hermitian quantum many-body scars against external fields, reveal the non-Hermitian quantum criticality and eventually set up the whole phase diagram. The possible connection to the open quantum many-body systems is also explored. Our findings offer insights for realizing long-lived coherent states in non-Hermitian many-body systems.
The recent discovery of persistent revivals in the Rydberg-atom quantum simulator has revealed a weakly ergodicity-breaking mechanism dubbed quantum many-body scars, which are a set of nonthermal states embedded in otherwise thermal spectra. Until now, such a mechanism has been mainly studied in Hermitian systems. Here, we establish the non-Hermitian quantum many-body scars and systematically characterize their nature from dynamic revivals, entanglement entropy, physical observables, and energy level statistics. Notably, we find the non-Hermitian quantum many-body scars exhibit significantly enhanced coherent revival dynamics when approaching the exceptional point. The signatures of non-Hermitian scars switch from the real-energy axis to the imaginary-energy axis after a real-to-complex spectrum transition driven by increasing non-Hermiticity, where an exceptional point and a quantum tricritical point emerge simultaneously. We further examine the stability of non-Hermitian quantum many-body scars against external fields, reveal the non-Hermitian quantum criticality and eventually set up the whole phase diagram. The possible connection to the open quantum many-body systems is also explored. Our findings offer insights for realizing long-lived coherent states in non-Hermitian many-body systems.
Unraveling the mechanisms of ergodicity breaking in complex quantum systems is a central pursuit in nonequilibrium physics. In this work, we investigate a one-dimensional spin model featuring a tunable long-range hopping term,
Hn, which introduces nonlocal interactions and bridges the gap between Hermitian and non-Hermitian regimes. Through a systematic analysis of level-spacing statistics, Krylov complexity, and entanglement entropy, we demonstrate that
Hn acts as a universal control parameter driving the transition from integrability to quantum chaos. Specifically, increasing the strength of
Hn induces a crossover from Poissonian to Gaussian Orthogonal Ensemble statistics in the Hermitian limit, and similarly triggers chaotic dynamics in the non-Hermitian case. Most remarkably, despite the onset of global chaos, we identify a tower of exact nonthermal eigenstates that evade thermalization. These states survive as robust quantum many-body scars, retaining low entanglement and coherent dynamics even under strong non-Hermitian perturbations. Our findings reveal a universal mechanism by which long-range and non-Hermitian effects reshape quantum ergodicity, offering new pathways for preserving quantum coherence in complex many-body systems.