Recent advances in programmable quantum simulators have enabled the realization of irregular interaction networks, which natural crystal lattices cannot provide, together with time-resolved observation of quantum many-body dynamics. Understanding the nonequilibrium states that emerge from such networks has only just begun, and whether quantum many-body scar states can emerge in them remains open. Here, focusing on a quantum Ising spin system with random interaction networks under a weak transverse field, we introduce the flippability, the fraction of flippable spins, and present phenomenological laws that predict the emergence of quantum many-body scar states from the network structure. As the flippability increases, the Hilbert space becomes less fragmented. The largest kinetically accessible subspace shows nonintegrable level statistics, yet hosts a few eigenstates with abnormally low participation entropy, signalling scar states. Real-time dynamics from Fock states confirm these signatures: systems with higher flippability tend toward thermalization, whereas a few initial states show anomalously nonthermal dynamics. The flippability thus links the interaction-network structure of the Hamiltonian to nonequilibrium many-body dynamics without translational invariance, and may apply to other kinetically constrained quantum systems.
Recent advances in programmable quantum simulators have enabled the realization of irregular interaction networks, which natural crystal lattices cannot provide, together with time-resolved observation of quantum many-body dynamics. Understanding the nonequilibrium states that emerge from such networks has only just begun, and whether quantum many-body scar states can emerge in them remains open. Here, focusing on a quantum Ising spin system with random interaction networks under a weak transverse field, we introduce the flippability, the fraction of flippable spins, and present phenomenological laws that predict the emergence of quantum many-body scar states from the network structure. As the flippability increases, the Hilbert space becomes less fragmented. The largest kinetically accessible subspace shows nonintegrable level statistics, yet hosts a few eigenstates with abnormally low participation entropy, signalling scar states. Real-time dynamics from Fock states confirm these signatures: systems with higher flippability tend toward thermalization, whereas a few initial states show anomalously nonthermal dynamics. The flippability thus links the interaction-network structure of the Hamiltonian to nonequilibrium many-body dynamics without translational invariance, and may apply to other kinetically constrained quantum systems.
Abstract 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, however its experimental realization remains limited to the Z2 state in a Rydberg atom system. Here we realize unconventional many-body scarring in a Bose--Hubbard quantum simulator with a previously unknown initial condition -- the unit-filling state. Our measurements of entanglement entropy illustrate that scarring traps the many-body system in a low-entropy subspace. Further, we develop a quantum interference protocol to probe out-of-time correlations, and demonstrate the system's return to the vicinity of the initial state by measuring single-site fidelity. Our work makes the resource of scarring accessible to a broad class of ultracold-atom experiments, and it allows to explore its relation to constrained dynamics in lattice gauge theories, Hilbert space fragmentation, and disorder-free localization.
Non-ergodic quantum many-body dynamics offers a route to persistent quantum coherence far from equilibrium, beyond the conventional expectations of thermalizing statistical mechanics. Most known examples have been identified through intuition, analogy, or numerical search, rather than by systematic Hamiltonian design. This leaves few general methods for engineering robust non-ergodic dynamics in disorder-free interacting quantum many-body systems, especially in higher dimensions where enhanced connectivity generally disfavors ergodicity breaking. Here, we use an eigenstate-to-Hamiltonian construction approach to systematically engineer two-dimensional quantum spin Hamiltonians with tunable non-ergodic properties. Starting from a common parent model and input eigenstate, we construct two target Hamiltonians on the square lattice that differ in their interaction geometry: axial versus diagonal. We show that the resulting interaction geometry and coupling pattern control the Hilbert-space structure and dynamics. The axial model forms a connected Hilbert-space network and exhibits an anisotropy-driven crossover from ergodic to non-ergodic behavior through the suppression of resonances. In contrast, the diagonal model exhibits Hilbert-space fragmentation and, within its largest irreducible sector, signatures of quantum many-body scar dynamics including towers of highly localized, low-entanglement eigenstates, and long-lived coherent revivals. These results establish a direct link between Hamiltonian design, Hilbert-space network structure, and emergent non-ergodic dynamics.
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.
The observations of persistent revivals in the Rydberg atom chain have revealed a weak ergodicity breaking mechanism known as quantum many-body scars, which is typically a collection of states with low entanglement embedded in otherwise thermal spectra. Here, by applying a generic formalism, we reveal a direct evolution from the quantum many-body scars to the multiple inverted quantum many-body scars, i.e., different sets of excited states with volume-law entanglement entropy embedded in a sea of states with area-law entanglement. When increasing the disorder strength, a series of exact eigenstates, acting as conventional quantum many-body scars in a regime of weak disorder, remain unchanged. Around each of these states, the inverted quantum many-body scars are introduced by the increased disorder. Moreover, the strong disorder also gives rise to additional sets of inverted quantum many-body scars with their energies concentrating in the middle of the exact eigenstates. As a result, all the multiple inverted quantum many-body scars are approximately equidistant in energy, reminiscent of conventional quantum many-body scarred states. Despite being the measure-zero states in the whole spectrum, these inverted quantum many-body scarred states significantly influence nonequilibrium dynamics in the large disorder regime. Random thermal states in a specific subspace show periodic revivals in the fidelity dynamics, while the typical charge-density-wave states exhibit persistent imbalance dynamics. We further examine the stability of the conventional and the inverted quantum many-body scars against the external random field. Our findings expand the variety of nonthermal systems and draw a connection between the weak violation of ergodicity and that of nonergodicity.
The transverse-field Ising model is one of the fundamental models in quantum many-body systems, yet a full understanding of its dynamics remains elusive in higher than one dimension. Here, we show for the first time the breakdown of ergodicity in d-dimensional Ising models with a weak transverse field in a prethermal regime. We demonstrate that novel Hilbert-space fragmentation occurs in the effective nonintegrable model with d≥2 as a consequence of only one emergent global conservation law of the domain wall number. Our results indicate nontrivial initial-state dependence for nonequilibrium dynamics of the Ising models with a weak transverse field.
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.