Non-equilibrium non-Markovian steady-states in open quantum many-body systems: Persistent oscillations in Heisenberg quantum spin chains

We investigate the effect of a non-Markovian, structured reservoir on an open Heisenberg spin chain. We establish a coherent self-feedback mechanism as the reservoir couples frequency-dependent to the spin chain. Thus, loss and driving take place due to the interaction of the spin chain with its own past. This new paradigm of non-Markovian imposed boundary-driving allows to discuss a new kind of non-equilibrium steady-state. We show that for certain parameters even in the long-time limit persistent oscillations occur within the chain. Moreover, we demonstrate that the conditions for these oscillations and excitation trapping depend on the characteristics of the chain, thus making it possible to characterize a chain by detection of its emitted signal under influence of self-feedback.