Thermalization in closed quantum systems and its breakdown are central to understanding the emergence of statistical behavior in isolated many-body systems. Kinetic constraints can hinder thermalization by restricting the allowed dynamics and giving rise to non-ergodic behavior. While various aspects of ergodicity breaking in kinetically constrained models have been extensively studied in Hermitian systems, their behavior in non-Hermitian kinetically constrained models remains less explored. In particular, the inequivalence of left and right eigenstate ensembles in non-Hermitian systems raises the question of whether they exhibit qualitatively different dynamical and eigenstate properties. In this work, we study non-Hermitian generalizations of the paradigmatic PXP and PPXPP models, focusing on their Krylov complexity, eigenstate structure, and dynamics. By exploiting the Arnoldi's algorithm, we find distinct behavior of Krylov complexity in the left and right eigenstate ensembles as non-Hermiticity is increased: in the right ensemble, it exhibits persistent oscillations with an increasing period, while in the left ensemble, it gradually saturates. The characteristic arch-shaped profile of the Arnoldi coefficients is also modified differently in the two ensembles, with a Hermitian-like arch re-emerging in the left ensemble at large non Hermiticity. Additionally, in the non-Hermitian PXP model, the right ensemble retains the characteristic scar structure, while the left ensemble develops additional non-scar eigenstates with anomalously low entanglement and large overlap with the vacuum state. These findings reveal that non-Hermiticity can affect Krylov dynamics and eigenstate structure differently in the left and right ensembles, demonstrating the need to treat them separately when characterizing non-Hermitian kinetically constrained systems.
Thermalization in closed quantum systems and its breakdown are central to understanding the emergence of statistical behavior in isolated many-body systems. Kinetic constraints can hinder thermalization by restricting the allowed dynamics and giving rise to non-ergodic behavior. While various aspects of ergodicity breaking in kinetically constrained models have been extensively studied in Hermitian systems, their behavior in non-Hermitian kinetically constrained models remains less explored. In particular, the inequivalence of left and right eigenstate ensembles in non-Hermitian systems raises the question of whether they exhibit qualitatively different dynamical and eigenstate properties. In this work, we study non-Hermitian generalizations of the paradigmatic PXP and PPXPP models, focusing on their Krylov complexity, eigenstate structure, and dynamics. By exploiting the Arnoldi's algorithm, we find distinct behavior of Krylov complexity in the left and right eigenstate ensembles as non-Hermiticity is increased: in the right ensemble, it exhibits persistent oscillations with an increasing period, while in the left ensemble, it gradually saturates. The characteristic arch-shaped profile of the Arnoldi coefficients is also modified differently in the two ensembles, with a Hermitian-like arch re-emerging in the left ensemble at large non Hermiticity. Additionally, in the non-Hermitian PXP model, the right ensemble retains the characteristic scar structure, while the left ensemble develops additional non-scar eigenstates with anomalously low entanglement and large overlap with the vacuum state. These findings reveal that non-Hermiticity can affect Krylov dynamics and eigenstate structure differently in the left and right ensembles, demonstrating the need to treat them separately when characterizing non-Hermitian kinetically constrained systems.
Scar eigenstates in a many-body system refers to a small subset of non-thermal finite energy density eigenstates embedded into an otherwise thermal spectrum. This novel non-thermal behaviour has been seen in recent experiments simulating a one-dimensional PXP model with a kinetically-constrained local Hilbert space realised by a chain of Rydberg atoms. We probe these small sets of special eigenstates starting from particular initial states by computing the spread complexity associated to time evolution of the PXP hamiltonian. Since the scar subspace in this model is embedded only loosely, the scar states form a weakly broken representation of the Lie algebra. We demonstrate why a careful usage of the forward scattering approximation (FSA), instead of any other method, is required to extract the most appropriate set of Lanczos coefficients in this case as the consequence of this approximate symmetry. Only such a method leads to a well defined notion of a closed Krylov subspace and consequently, that of spread complexity. We show this using three separate initial states, namely|Z2⟩,|Z3⟩and the vacuum state, due to the disparate classes of scar states hosted by these sectors. We also discuss systematic methods of remedying the imperfections in the FSA setup stemming from these approximate symmetries.
Quantum many-body scars are atypical, highly nonthermal eigenstates embedded in a sea of thermal eigenstates that have been observed in, for example, kinetically constrained quantum many-body models. These special eigenstates are characterized by a bipartite entanglement entropy that scales as most logarithmically with the subsystem size. We use numerical optimization techniques to investigate if quantum many-body scars of the experimentally relevant PXP model can be well approximated by Gaussian states. Gaussian states are described by a number of parameters that scales quadratically with system size, thereby having a much lower complexity than generic quantum many-body states, for which this number scales exponentially. We find that while quantum many-body scars can typically be well approximated by (symmetrized) Gaussian states, this is not the case for ergodic (thermal) eigenstates. This observation suggests that the non-ergodic part of the PXP Hamiltonian is related to certain quadratic parent Hamiltonians, thereby hinting on the origin of the quantum many-body scars.
Kinetic constraints in quantum many-body systems strongly restrict the accessible Hilbert space, giving rise to highly nontrivial dynamical behavior. In recent years, such systems have attracted growing interest as they provide insight into mechanisms of thermalization and into regimes where thermalization fails. In this work, we study a family of rule-based kinetically constrained models, including the celebrated Quantum Game of Life, from the perspective of quantum complexity, with a focus on entanglement, nonstabilizerness, and quantum chaos. Using spectral diagnostics such as level statistics and spectral form factors, we show that these models exhibit robust chaotic behavior while simultaneously supporting both strong and weak Hilbert-space fragmentation and quantum many-body scar states. Our results reveal that the nature of Hilbert-space fragmentation can be tuned qualitatively from strong to weak fragmentation and ultimately to its absence, within a single family of models through simple variations of the underlying kinetic rules. To further elucidate the structure of these fragmented subspaces, we characterize them through their ability to generate quantum resources. In particular, we show that resource-generation capacity does not necessarily correlate with the dimensionality of a fragmented sector, and that entanglement structure and the ability to generate nonstabilizerness provide effective diagnostics for distinguishing dynamically disconnected sectors, including those supporting nonthermal scarred dynamics. Our work thus places kinetically constrained models within a broader and more general framework, not limited to Rydberg blockade based constraints only, and demonstrates that simple variations in underlying rules can lead to qualitatively distinct static and dynamical regimes including chaotic, fragmented, and scarred phases.
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.
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.