Exceptional Stationary State in a Dephasing Many-Body Open Quantum System

We study a dephasing many-body open quantum system that hosts, together with the infinite-temperature state, another additional stationary state, that is associated with a nonextensive strong symmetry. This state, that is a pure dark state, is exceptional in that it retains memory of the initial condition, whereas any orthogonal state evolves toward the infinite-temperature state erasing any information on the initial state. We discuss the approach to stationarity of the model focusing in particular on the fate of interfaces between the two states. A simple model based on a membrane picture helps developing an effective large-scale theory, which is different from the usual hydrodynamics since no extensive conserved quantities are present. The fact that the model reaches stationary properties on timescales that diverge with the system size, while the Lindbladian gap is finite, is duly highlighted. We point out the reasons for considering these exceptional stationary states as quantum many-body scars in the open system framework.