Signatures of integrability in the dynamics of Rydberg-blockaded chains

A recent experiment on a 51-atom Rydberg-blockaded chain observed anomalously long-lived temporal oscillations of local observables after quenching from an antiferromagnetic initial state. This coherence is surprising as the initial state should have thermalized rapidly to infinite temperature. In this Rapid Communication, we show that the experimental Hamiltonian exhibits nonthermal behavior across its entire many-body spectrum, with similar finite-size scaling properties as models proximate to integrable points. Moreover, we construct an explicit small local deformation of the Hamiltonian which enhances both the signatures of integrability and the coherent oscillations observed after the quench. Our results suggest that a parent proximate integrable point controls the early-to-intermediate time dynamics of the experimental system. The distinctive quench dynamics in the parent model could signal an unconventional class of integrable system.