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arXiv:2602.21962 · Physical review. B./Physical review. B

Tighter thermalization bounds for perturbed quantum many-body scars

Mao Meng-yun, Zhixiang Sun, Wen‐Long You

Published Feb 10, 2026• 0 citations
arXivHTMLPDF

Abstract

Quantum many-body scars (QMBS) are exceptional eigenstates that defy thermalization, enabling long-lived coherent dynamics in strongly interacting systems. However, their stability under perturbations remains inadequately understood. In this work, we derive improved lower bounds on the thermalization time of QMBS under local perturbations with strength $λ$. Using both numerical simulations and analytical reasoning, we show that exact QMBS exhibit slow thermalization, with a timescale scaling as $τ\sim \mathcal{O}(λ^{-1/d})$ owing to the stabilizing restricted spectrum-generating algebra (RSGA), which is a significant improvement over previous bounds (e.g., $τ\sim \mathcal{O}(λ^{-1/(d+1)})$). Counterintuitively, approximate QMBS can thermalize even more slowly under generic perturbations, exhibiting $τ\sim \mathcal{O}(λ^{-2})$ scaling due to second-order perturbative effects in the absence of such protective structure. These distinct thermalization behaviors clarify how exact and approximate scars maintain coherence. Our work advances previous findings by establishing a tighter bound on the thermalization time, clarifying when scarred dynamics remain long-lived under weak but generic perturbations.

DOI
10.1103/2hjm-m1v9

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Quantum many-body scars (QMBS) are exceptional eigenstates that defy thermalization, enabling long-lived coherent dynamics in strongly interacting systems. However, their stability under perturbations remains inadequately understood. In this work, we derive improved lower bounds on the thermalization time of QMBS under local perturbations with strength λλλ. Using both numerical simulations and analytical reasoning, we show that exact QMBS exhibit slow thermalization, with a timescale scaling as τ∼O(λ−1/d)τ\sim \mathcal{O}(λ^{-1/d})τ∼O(λ−1/d) owing to the stabilizing restricted spectrum-generating algebra (RSGA), which is a significant improvement over previous bounds (e.g., τ∼O(λ−1/(d+1))τ\sim \mathcal{O}(λ^{-1/(d+1)})τ∼O(λ−1/(d+1))). Counterintuitively, approximate QMBS can thermalize even more slowly under generic perturbations, exhibiting τ∼O(λ−2)τ\sim \mathcal{O}(λ^{-2})τ∼O(λ−2) scaling due to second-order perturbative effects in the absence of such protective structure. These distinct thermalization behaviors clarify how exact and approximate scars maintain coherence. Our work advances previous findings by establishing a tighter bound on the thermalization time, clarifying when scarred dynamics remain long-lived under weak but generic perturbations.
Quantum many-body scars are special eigenstates that violate the eigenstate thermalization hypothesis while residing at finite energy density along with thermalizing eigenstates. The spin-1 XY model is known to host a family of such exceptional states originating from long-lived quasiparticle excitations that exhibit anomalously low entanglement entropy and long-time periodic revivals, resulting in weak ergodicity breaking. We study the stability of these scarred states against typical U(1) symmetry preserving perturbation in the XY chain. While perturbation theory can describe the deformed scar states at small system sizes, finite-size scaling of the perturbation matrix elements indicate that the scars ultimately thermalize in larger chains. Nonetheless, we demonstrate that the long-range order associated with the scars decays under the perturbation, and we estimate the relaxation timescale of oscillatory dynamics in certain local observables to be of order λ−2λ^{-2}λ−2, where λλλ is the perturbation strength.
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.
Abstract Generic closed quantum many-body systems tend to thermalize, a phenomenon known as quantum ergodicity, where initial local information scrambles into the full space. A paradigmatic exception is many-body localization (MBL), where disorder prevents thermalization and breaks ergodicity strongly. While environmental dissipation is generally expected to delocalize such systems, this consequence has recently been challenged. Here we show that local dissipative operators can instead stabilize weak ergodicity breaking in systems with quantum many-body scars (QMBS). These operators drive the system into steady states dominated by scarred eigenstates. Furthermore, we show that this tailored dissipation induces robust dynamic revivals, even in the presence of local dephasing noise. We propose an experimental realization using a cold atomic setup. Our findings make ergodicity-breaking signatures directly observable in dissipative dynamics and open avenues for preparing long-lived QMBS states with coherent dynamics.
Abstract Quantum many-body scars (QMBSs) are atypical eigenstates in otherwise nonintegrable systems that weakly break ergodicity, exhibiting nonthermal dynamics and long-lived periodic revivals. However, implementing QMBS in non-Hermitian systems remains a significant challenge, as it demands a deep understanding of the influence of exceptional points (EPs) on quantum many-body dynamics, especially higher-order EPs. Here, we use single-photon interference to demonstrate that experimentally controlled non-Hermitian dissipation stabilizes and enhances scarred dynamics, realizing nearly perfect, high-fidelity revival. These ideas can be exemplified in quantum systems that support scarred dynamics. In the non-Hermitian regime, symmetry-promoted exceptional points confine the dynamics to robust nonthermal subspaces, enabling high-fidelity scarred revivals over an extended parameter range. These results establish non-Hermitian quantum engineering as a versatile strategy for creating and sustaining perfect quantum scars, offering pathways for quantum-enhanced metrology, coherent state preparation, and fault-tolerant quantum information processing.
Quantum many-body scars (QMBS) are exceptional energy eigenstates of quantum many-body systems associated with violations of thermalization for special nonequilibrium initial states. Their various systematic constructions require fine-tuning of local Hamiltonian parameters. In this work, we demonstrate that long-range interacting quantum spin systems generically host robust QMBS. We analyze spectral properties upon raising the power-law decay exponent α of spin-spin interactions from the solvable permutationally symmetric limit α = 0 . First, we numerically establish that, despite the fact that spectral signatures of chaos appear for infinitesimal α , the towers of α = 0 energy eigenstates with large collective spin are smoothly deformed as α is increased and exhibit characteristic QMBS features. To elucidate the nature and fate of these states in larger systems, we introduce an analytical approach based on mapping the spin Hamiltonian onto a relativistic quantum rotor nonlinearly coupled to an extensive set of bosonic modes. We analytically solve for the eigenstates of this interacting impurity model by means of a novel polaron-type canonical transformation and show their self-consistent localization in large-spin sectors of the original Hamiltonian for 0 < α < d (with d = spatial dimension of the lattice ). Our theory unveils the stability mechanism of such QMBS for an arbitrary system size and predicts instances of its breakdown, e.g., near dynamical critical points or in the presence of semiclassical chaos, which we verify numerically in long-range quantum Ising chains. As a by-product, we find a predictive criterion for the presence or absence of heating under periodic driving for 0 < α < d , beyond existing Floquet-prethermalization theorems.
Quantum many-body scars (QMBSs) represent a weak ergodicity-breaking phenomenon that defies the common scenario of thermalization in closed quantum systems. They are often regarded as a many-body analog of quantum scars (QSs)—a single-particle phenomenon in quantum chaos—due to their superficial similarities. However, unlike QSs, a clear connection between QMBSs and classical chaos has remained elusive. It has nevertheless been speculated that in an appropriate semiclassical limit, QMBSs should have a correspondence to weakly unstable periodic orbits. In this paper, I present a counterexample to this conjecture by studying a bosonic model with a large number of flavors. The dynamics of out-of-time-ordered correlators (OTOCs) suggest that QMBS do not display chaotic behavior in the semiclassical limit. In contrast, chaotic dynamics are expected for initial states not associated with QMBS. Interestingly, the anomalous OTOC dynamics persist even under weak perturbations that eliminate the scarred eigenstates, suggesting a certain robustness in the phenomenon.