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Physica Scripta

Stability of quantum many-body scars on PXP model

Alessandra Chioquetta, Raphael C. Drumond

Published May 19, 2025• 2 citations
Publisher

Abstract

Abstract We investigated the stability of quantum many-body scars under perturbations using a PXP model. Using numerical simulations, we analyzed the fidelity and correlation functions of the system to track its evolution and assess the persistence of revivals. We explored two distinct types of perturbations: imperfections in the initial state, which naturally arise in experimental settings, and disorder in the Hamiltonian, which was introduced as a computational tool to probe the system’s response to external disturbances. We found that while certain initial state modifications can partially stabilize oscillations by restricting the system’s accessible dynamics, others accelerate thermalization by increasing overlap with the full eigenstate spectrum. Similarly, disorder in the Hamiltonian gradually suppresses revivals and enhances thermalization, but scars demonstrate robustness for small perturbations. Our results provide insights into the conditions under which quantum many-body scars persist, offering valuable implications for experimental realizations and controlled quantum dynamics.

DOI
10.1088/1402-4896/adda9d

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Stability of quantum many-body scars on PXP model

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Bridging quantum criticality via many-body scarring

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Quantum dynamics in certain kinetically-constrained systems can display a strong sensitivity to the initial condition, wherein some initial states give rise to persistent quantum revivals---a type of weak ergodicity breaking known as ``quantum many-body scarring'' (QMBS). Recent work [Yao, Pan, Liu, and Zhai, Phys. Rev. B 105, 125123 (2022)] pointed out that QMBS gets destroyed by tuning the system to a quantum critical point, echoing the disappearance of long-range order in the system's ground state at equilibrium. Here we show that this picture can be much richer in systems that display QMBS dynamics from a continuous family of initial conditions: As the system is tuned across the critical point while at the same time deforming the initial state, the dynamical signatures of QMBS at intermediate times can undergo an apparently smooth evolution across the equilibrium phase transition point. We demonstrate this using the PXP model---a paradigmatic model of QMBS that has recently been realized in Rydberg atom arrays as well as ultracold bosonic atoms in a tilted optical lattice. Using exact diagonalization and matrix product state methods, we map out the dynamical phase diagram of the PXP model with the quenched chemical potential. We demonstrate the existence of a continuous family of initial states that give rise to QMBS and formulate a ramping protocol that can be used to prepare such states in experiment. Our results show the ubiquity of scarring in the PXP model and highlight its intriguing interplay with quantum criticality.

arXiv:2301.03631•Physical review. B./Physical review. B•Jun 5, 2023•20 citations
Abstract We investigated the stability of quantum many-body scars under perturbations using a PXP model. Using numerical simulations, we analyzed the fidelity and correlation functions of the system to track its evolution and assess the persistence of revivals. We explored two distinct types of perturbations: imperfections in the initial state, which naturally arise in experimental settings, and disorder in the Hamiltonian, which was introduced as a computational tool to probe the system’s response to external disturbances. We found that while certain initial state modifications can partially stabilize oscillations by restricting the system’s accessible dynamics, others accelerate thermalization by increasing overlap with the full eigenstate spectrum. Similarly, disorder in the Hamiltonian gradually suppresses revivals and enhances thermalization, but scars demonstrate robustness for small perturbations. Our results provide insights into the conditions under which quantum many-body scars persist, offering valuable implications for experimental realizations and controlled quantum dynamics.
We investigate the stability of quantum many-body scars under perturbations, within the PXP model. We numerically compute the fidelity and average correlations to monitor the state evolution and to identify revivals. The results indicate that, on the one hand, the entanglement entropy of PXP scars exhibit great sensitivity, in the sense that their profile approaches the ones expected for thermal states already for very small perturbations. On the other hand, other scar signatures, such as the revivals of states having large overlap with scars, show remarkable robustness. Additionally, we examined the effects of minor disturbances on initial states that previously exhibited high overlap with scars and consistent revivals. Our analysis revealed that different types of disturbances can induce markedly different behaviors, such as partially "freezing" the chain, leading to sustained oscillations, or accelerating the process of thermalization.
Persistent revivals recently observed in Rydberg atom simulators have challenged our understanding of thermalization and attracted much interest to the concept of quantum many-body scars (QMBSs). QMBSs are non-thermal highly excited eigenstates that coexist with typical eigenstates in the spectrum of many-body Hamiltonians, and have since been reported in multiple theoretical models, including the so-called PXP model, approximately realized by Rydberg simulators. At the same time, questions of how common QMBSs are and in what models they are physically realized remain open. In this Letter, we demonstrate that QMBSs exist in a broader family of models that includes and generalizes PXP to longer-range constraints and states with different periodicity. We show that in each model, multiple QMBS families can be found. Each of them relies on a different approximate su(2) algebra, leading to oscillatory dynamics in all cases. However, in contrast to the PXP model, their observation requires launching dynamics from weakly entangled initial states rather than from a product state. QMBSs reported here may be experimentally probed using Rydberg atom simulator in the regime of longer-range Rydberg blockades.
Quantum scars are nonthermal eigenstates characterized by low entanglement entropy, initially detected in systems subject to nearest-neighbor Rydberg blockade, the so-called PXP model. While most of these special eigenstates elude an analytical description and seem to hybridize with nearby thermal eigenstates for large systems, some of them can be written as matrix product states with size-independent bond dimension. We study the response of these exact quantum scars to perturbations by analyzing the scaling of the fidelity susceptibility with system size. We find that some of them are anomalously stable at first order in perturbation theory, in sharp contrast to the eigenstate thermalization hypothesis. However, this stability seems to break down when all orders are taken into account. We further investigate models with larger blockade radius and find a set of exact quantum scars that we write down analytically and compare with the PXP exact eigenstates. We show that they exhibit the same robustness against perturbations at first order.
Recently a class of quantum systems exhibiting weak ergodicity breaking has attracted much attention. These systems feature in the energy spectrum a special band of eigenstates called quantum many-body scar states. One prototype model that is known to host scar states is the so-called PXP model. In this work we study the fate of quantum many-body scar states in a 2D PXP model against random disorders. We show that in both the square lattice and the honeycomb lattice the scar states can persist up to a finite disorder strength, before eventually being erased by the disorder. We further study the localization properties of the system in the presence of even stronger disorders and show that whether a full localization transition occurs depends on the type of disorder we introduce. Our study thus reveals the fascinating interplay between disorder and quantum many-body scarring in a 2D system.
Quantum many-body scars are atypical, non-thermal eigenstates that constitute a mechanism of weak ergodicity breaking, yet their stability in realistic, open quantum systems remains an outstanding question. We investigate the interplay between stability and quantum information dynamics within the PXP model subjected to local dissipation. Employing a non-Hermitian formalism, we analytically demonstrate and numerically corroborate that scar eigenstates possess intrinsic decay rates parametrically smaller than those of the surrounding chaotic bulk, revealing a pronounced stability hierarchy. This spectral robustness is a direct manifestation of the approximate algebraic structure underpinning the scars. This resilience has direct dynamical consequences. We find a suppression of information scrambling, quantified by the out-of-time-order correlator (OTOC), for dynamics initiated from scar-like states. Analysis of entanglement dynamics reveals that quantum correlations in scar states persist for longer timescales under weak dissipation. These results demonstrate that algebraic confinement reduces the susceptibility of scar states to both dissipation and chaotic scrambling; the signature of this resilience is a persistent suppression of the scrambling rate and the presence of coherent oscillations, not a uniformly longer signal lifetime.
Quantum dynamics in certain kinetically-constrained systems can display a strong sensitivity to the initial condition, wherein some initial states give rise to persistent quantum revivals---a type of weak ergodicity breaking known as ``quantum many-body scarring'' (QMBS). Recent work [Yao, Pan, Liu, and Zhai, Phys. Rev. B 105, 125123 (2022)] pointed out that QMBS gets destroyed by tuning the system to a quantum critical point, echoing the disappearance of long-range order in the system's ground state at equilibrium. Here we show that this picture can be much richer in systems that display QMBS dynamics from a continuous family of initial conditions: As the system is tuned across the critical point while at the same time deforming the initial state, the dynamical signatures of QMBS at intermediate times can undergo an apparently smooth evolution across the equilibrium phase transition point. We demonstrate this using the PXP model---a paradigmatic model of QMBS that has recently been realized in Rydberg atom arrays as well as ultracold bosonic atoms in a tilted optical lattice. Using exact diagonalization and matrix product state methods, we map out the dynamical phase diagram of the PXP model with the quenched chemical potential. We demonstrate the existence of a continuous family of initial states that give rise to QMBS and formulate a ramping protocol that can be used to prepare such states in experiment. Our results show the ubiquity of scarring in the PXP model and highlight its intriguing interplay with quantum criticality.