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

Recent realization of a kinetically constrained chain of Rydberg atoms by Bernien, [Nature (London) 551, 579 (2017)NATUAS0028-083610.1038/nature24622] resulted in the observation of unusual revivals in the many-body quantum dynamics. In our previous work [C. J. Turner, Nat. Phys. 14, 745 (2018)10.1038/s41567-018-0137-5], 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 nonergodic 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 subthermal 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.