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arXiv:2407.14691

Stability of quantum many-body scars on PXP model

Alessandra Chioquetta, Raphael C. Drumond

Published Jul 19, 2024• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.2407.14691

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arXiv:2303.04259•Physical review. B./Physical review. B•Jun 12, 2023•17 citations
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.
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.
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.
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.
To provide a physical example of quantum scars, we study the many-body scars in the spin-1 Kitaev chain where the so-called PXP Hamiltonian is exactly embedded in the spectra. Regarding the conserved quantities, the Hilbert space is fragmented into disconnected subspaces and we explore the associated constrained dynamics. The continuous revivals of the fidelity and the entanglement entropy when the initial state is prepared in $|{\mathbb{Z}}_{k}\ensuremath{\rangle}$ (k=2,3k=2,3k=2,3) state illustrate the essential physics of the PXP model. We study the quantum phase transitions in the one-dimensional spin-1 Kitaev-Heisenberg model using the density-matrix renormalization group and Lanczos exact diagonalization methods, and determine the phase diagram. We parametrize the two terms in the Hamiltonian by the angle $\ensuremath{\phi}$, where the Kitaev term is $K\ensuremath{\equiv}sin(\ensuremath{\phi})$ and competes with the Heisenberg $J\ensuremath{\equiv}cos(\ensuremath{\phi})$ term. One finds a rich ground-state phase diagram as a function of the angle $\ensuremath{\phi}$. Depending on the ratio $K/J\ensuremath{\equiv}tan(\ensuremath{\phi})$, the system either breaks the symmetry to one of distinct symmetry broken phases, or preserves the symmetry in a quantum spin-liquid phase with frustrated interactions. We find that the scarred state is stable for perturbations which obey Z2{\mathbb{Z}}_{2}Z2​-symmetry, while it becomes unstable against Heisenberg-type 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.
Experimental observation of coherent oscillations in a Rydberg atom chain [H. Bernien et al., Nature (London) 551, 579 (2017)] has led to the discovery of quantum many-body scars (QMBSs) which is a new paradigm for ergodicity breaking. The experimental findings in the Rydberg chain can be well captured by a kinetically constrained model called the ``PXP'' model, which has been shown to host the eigenstate thermalization hypothesis (ETH)-violating scar states in the middle of the spectrum. Much effort has been put into identifying similar kinetically restricted systems that show a violation of ETH. In this paper, we study the QMBSs that can arise in one such model, namely the spin-1 Kitaev chain, where owing to some conserved quantities, the Hilbert space gets fragmented into unequal disconnected subspaces. Recently, You et al. [Phys. Rev. Res. 4, 013103 (2022)] showed that the ground state sector of this chain can be mapped exactly onto the prototypical PXP model and thus hosts QMBSs. Here, we demonstrate that the phenomenon of scarring is also present in other sectors, and in particular, we identify a sector that exhibits substantially more scarring than the ground state one. We propose an initial state and numerically demonstrate that its fidelity revivals are pronounced and longer lived than those in the PXP model.