Open-system quantum many-body scars: a theory

Abstract: In this work, we undertake the problem of formally introducing a notion of quantum many-body scarring in open quantum systems governed by the Lindblad equation. To this goal, we rely on the commutant-algebra framework for the description of strong symmetries to introduce the unconventional strong-symmetry structure leading to the existence of anomalous stationary states, which we dub open-system quantum many-body scars (OSQMBS), besides a typical infinite-temperature state. We provide several benchmarks of the theoretical predictions on the stationary-state manifold and on convergence to stationarity, as well as describe the time-evolution of off-diagonal coherences among the Hilbert space symmetry sectors identified by OSQMBS and their orthogonal complement. Moreover, we investigate the existence of asymptotic OSQMBS (AOSQMBS), the latter being states that, despite converging to the typical infinite-temperature state in the large-time limit, display anomalously-large relaxation time scales, which we thoroughly describe by means of the behavior of their fidelity as a function of time through proper scaling Ansaetze.