Quantum scarring enhances non-Markovianity of subsystem dynamics

Given that any subsystem of a closed out-of-equilibrium quantum system is an open quantum system, its dynamics (reduced from the full system's unitary evolution) can be either Markovian (memory-less) or non-Markovian, with the latter necessarily impeding the process of relaxation and thermalization. Seemingly independently, such non-ergodic dynamics occurs when an initial state has spectral weight on the so-called quantum scar states, which are non-thermalizing states embedded deep in the spectrum of otherwise thermal states. In this article, we present numerical evidence that the presence of quantum scars is a microscopic ingredient that enables and enhances non-Markovianity of the dynamics of subsystems. We exemplify this with the PXP model and its deformations which either enhance or erase the signatures of scarred dynamics when quenched from a simple product state that is known to have significant overlaps with the scarred subspace in the spectrum. By probing information backflows with the dynamical behaviour of the distances between temporally-separated states of small subsystems, systematic signatures of subsystem non-Markovianity in these models are presented, and it is seen that scarring-enhancing (erasing) deformations also exhibit enhanced (diminished) subsystem non-Markovianity. This sheds new light on the dynamical memories associated with quantum scarring, and opens interesting new questions at the interface of quantum scarring and an open quantum systems approach to investigating far-from-equilibrium and non-thermalizing isolated quantum many-body systems.