Quantum scarred eigenstates in a Rydberg atom chain: entanglement, breakdown of thermalization, and stability to perturbations

TL;DR

This paper investigates quantum scarred eigenstates in a Rydberg atom chain, revealing their atypical properties, partial thermalization, and robustness to certain perturbations, advancing understanding of non-ergodic behavior in many-body quantum systems.

Contribution

It provides a detailed analysis of quantum scarred eigenstates, their entanglement, and stability, introducing the forward scattering approximation to describe their structure and effects.

Findings

Most eigenstates show anomalous, slow thermalization.

Identified non-ergodic eigenstates that violate ETH and grow polynomially with system size.

Quantum scars are robust to compatible perturbations but destroyed by others.

Abstract

Recent realization of a kinetically-constrained chain of Rydberg atoms by Bernien et al. [Nature 551, 579 (2017)] resulted in the observation of unusual revivals in the many-body quantum dynamics. In our previous work [arXiv:1711.03528] such dynamics was attributed to the existence of "quantum scarred" eigenstates in the many-body spectrum of the experimentally realized model. Here we present a detailed study of the eigenstate properties of the same model. We find that the majority of the eigenstates exhibit anomalous thermalization: the observable expectation values converge to their Gibbs ensemble values, but parametrically slower compared to the predictions of the eigenstate thermalization hypothesis (ETH). Amidst the thermalizing spectrum, we identify non-ergodic eigenstates that strongly violate the ETH, whose number grows polynomially with system size. Previously, the same eigenstates were identified via large overlaps with certain product states, and were used to explain the revivals observed in experiment. Here we find that these eigenstates, in addition to highly atypical expectation values of local observables, also exhibit sub-thermal entanglement entropy that scales logarithmically with the system size. Moreover, we identify an additional class of quantum scarred eigenstates, and discuss their manifestations in the dynamics starting from initial product states. We use forward scattering approximation to describe the structure and physical properties of quantum-scarred eigenstates. Finally, we discuss the stability of quantum scars to various perturbations. We observe that quantum scars remain robust when the introduced perturbation is compatible with the forward scattering approximation. In contrast, the perturbations which most efficiently destroy quantum scars also lead to the restoration of "canonical" thermalization.