Quantum many-body scars (QMBSs) appear in a flat-band model with interactions on the sawtooth lattice. The flat-band model includes localized eigenstates within compact support, known as compact localized states (CLSs). Some characteristic many-body states can be constructed from the CLSs at a low filling on the flat band. These many-body states are degenerate. Starting with such degenerate states we concretely show how to construct multiple QMBSs with different eigenenergies embedded in the entire spectrum. If the degeneracy is lifted by introducing hopping modulation or weak perturbations, the states lifted by these ways can be viewed as multiple QMBSs. In this work, we focus on the study of the perturbation-induced QMBS. Perturbed states, which are connected to the exact QMBSs in the unperturbed limit, indicate common properties of conventional QMBS systems, that is, a subspace with subvolume- or area-law scaling entanglement entropy, which indicates the violation of the strong eigenstate thermalization hypothesis (ETH). Also for a specific initial state, slow-thermalization dynamics appears. We numerically demonstrate these subjects. The flat-band model with interactions is a characteristic example in nonintegrable systems with the violation of the strong ETH and the QMBS.
Quantum many-body scars (QMBSs) appear in a flat-band model with interactions on the sawtooth lattice. The flat-band model includes localized eigenstates within compact support, known as compact localized states (CLSs). Some characteristic many-body states can be constructed from the CLSs at a low filling on the flat band. These many-body states are degenerate. Starting with such degenerate states we concretely show how to construct multiple QMBSs with different eigenenergies embedded in the entire spectrum. If the degeneracy is lifted by introducing hopping modulation or weak perturbations, the states lifted by these ways can be viewed as multiple QMBSs. In this work, we focus on the study of the perturbation-induced QMBS. Perturbed states, which are connected to the exact QMBSs in the unperturbed limit, indicate common properties of conventional QMBS systems, that is, a subspace with subvolume- or area-law scaling entanglement entropy, which indicates the violation of the strong eigenstate thermalization hypothesis (ETH). Also for a specific initial state, slow-thermalization dynamics appears. We numerically demonstrate these subjects. The flat-band model with interactions is a characteristic example in nonintegrable systems with the violation of the strong ETH and the QMBS.
We show that a quantum scar state, an atypical eigenstate breaking eigenstate thermalization hypothesis embedded in a many-body energy spectrum, can be constructed in flat band systems. The key idea of our construction is to make use of orthogonal compact localized states. We concretely discuss our construction scheme, taking a sawtooth flat lattice system as an example, and numerically demonstrate the presence of a quantum scar state. Examples of higher-dimensional systems are also addressed. Our construction method of quantum scar has broad applications to various flat band systems.
Quantum many-body scars (QMBSs) are a novel paradigm for the violation of the eigenstate thermalization hypothesis—Hamiltonians of these systems exhibit mid-spectrum eigenstates that are equidistant in energy and which possess low entanglement and evade thermalization for long times. We present a novel approach to understanding the anomalous dynamical behavior in these systems. Specifically, we postulate that QMBS Hamiltonians H can generically be partitioned into a set of terms O a which do not commute over the entire Hilbert space, but commute to all orders within the subspace of scar states. All states in the scar subspace thus evolve according to a “broken unitary” U s ( t ) = ∏ a e − i O a t , where H = ∑ a O a , which provides a simple interpretation of the anomalous dynamical features exhibited by quantum scars; they evolve in time according to a simpler unitary operator allowing for revivals. It is found that the observed dynamical decoupling is often a direct consequence of simple local conditions, which when satisfied lead to recurring aspects of QMBSs, including equidistant eigenvalues, many-body revivals, and sub-volume-law entanglement entropy. Two classes of scar models emerge in this picture—those with a finite set of O a , as pertaining of, for instance, scars in the AKLT model, and those with an extensive set of such operators, such as eta pairing scar states in the Hubbard model. Besides discussing how many well-known scar models fit into the above picture, we show how the broken unitary formalism captures many known scar construction methods, known in the literature and generalizes others such as quasiparticles matrix product state (MPS) based methods, and the Shiraishi-Mori approach. Published by the American Physical Society 2024
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 phenomenon of quantum many-body scars (QMBS) has been studied both theoretically and experimentally, due to its unusual violation of the eigenstate thermalization hypothesis (ETH). In this paper, we extend the ETH to a description based on the grand canonical ensemble to depict the thermal properties of QMBS models. For this purpose, we embed the dynamics of kinetically constrained systems within a Lindblad-like master equation, and demonstrate that the violation of the ETH by scar eigenstates is related to their slow decay in the corresponding dissipative process. Within this open system description, we reformulate the ETH to demonstrate that both scar eigenstates and thermal ones exhibit thermalization governed by grand canonical statistics. Consequently, our revised ETH unifies scars and thermal states under a cohesive thermodynamic rule. Our work resolves the fundamental tension between constraint-induced nonergodicity and thermalization paradigms, establishing a unified route to generalized thermalization in quantum many-body systems.
Quantum many-body scars (QMBSs) in kinetically constrained systems provide a prominent example of weak ergodicity breaking beyond the eigenstate thermalization hypothesis (ETH). In this work we formulate an open-system perspective on constrained dynamics, where kinetic constraints are interpreted as a balance of information exchange between the system and an auxiliary environment. This viewpoint naturally introduces a quasiparticle number that characterizes the information balance and motivates a revised ETH for constrained systems. Specifically, the eigenstate expectation values of local observables can be approximated by a grand-canonical-like average defined on the energy-quasiparticle-number plane. For the off-diagonal part of local observables, the relevant density of states (DOS) is generalized to the same plane and controls the typical magnitude of off-diagonal matrix elements. The revised ETH accurately describes long-time averages and temporal fluctuations of local observables for both QMBSs and thermal dynamics. Within this framework, scarred dynamics arises from low-DOS regions on the energy-quasiparticle-number plane, where off-diagonal elements are less suppressed and the approximate spectrum-generating algebra becomes more pronounced. Our results provide a unified description of thermalization and QMBSs in kinetically constrained systems.
In this work, we will introduce the concept of quantum scarring. Quantum scarring refers to the states inside the chaotic parts of spectra, which significantly differ from predictions for chaotic states. In this work, we will focus on Quantum Many-Body Scars (QMBS), which deviate from the Eigenvector Thermalization Hypothesis (ETH) predictions. First, we will introduce the ETH and several ways in which the QMBS deviate from it; periodic revivals of non-eigenstate QMBS, anomalously low values of entanglement entropy, and localization of Husimi function in the classical limit. We will apply these methods to detect and study QMBS on coupled Lipkin models. 1