Robustness of quantum scarred states to the presence of disorder and external drives

Recent experiments in Rydberg atom quantum simulators have found unexpected coherent and persistent oscillations in an ergodic system at infinite temperature. The origin of such oscillations has been explained in terms of quantum scarred states that are embedded in an ergodic spectrum. We examine the robustness of such quantum scarred states to the presence of inhomogeneous potentials as well as the action of external drives. We focus on models that exhibit approximate SU(2) symmetries, such as the PXP model, and explore conditions under which the dynamics of the system remains non-ergodic. To do this, we evaluate diagnostic quantities such as the revival probability, the spatial entanglement, and the average spin dynamics. Finally, we discuss similarities with the disordered Heisenberg spin chain in a regime in which anomalous non-ergodic dynamics can also be obtained.