Absence of thermalization of free systems coupled to gapped interacting reservoirs

We study the thermalization of a small XX chain coupled to long, gapped XXZ leads at either side by observing the relaxation dynamics of the whole system. Using extensive tensor network simulations, we show that such systems, although not integrable, appear to show either extremely slow thermalization or even lack thereof since the two cannot be distinguished within the accuracy of our numerics. We show that the persistent oscillations observed in the spin current in the middle of the XX chain are related to eigenstates of the entire system located within the gap of the boundary chains. We find from exact diagonalization that some of these states remain strictly localized within the XX chain and do not hybridize with the rest of the system. The frequencies of the persistent oscillations determined by numerical simulations of dynamics match the energy differences between these states exactly. This has important implications for open systems, where the strongly interacting leads are often assumed to thermalize the central system. Our results suggest that, if we employ gapped systems for the leads, this assumption does not hold.