Localization spectrum of a bath-coupled generalized Aubry-André model in the presence of interactions

A generalization of the Aubry-Andr\'e model, the noninteracting Ganeshan-Pixley-Das Sarma model (GPD) introduced by Ganeshan et al. [Phys. Rev. Lett. 114, 146601 (2015)], is known analytically to possess a mobility edge, allowing both extended and localized eigenstates to coexist. This mobility edge has been hypothesized to survive in closed many-body interacting systems, giving rise to a new nonergodic metallic phase. In this work, coupling the interacting GPD model to a thermal bath, we provide direct numerical evidence for multiple qualitative behaviors in the parameter space of disorder strength and energy level. In particular, we look at the bath-induced saturation of entanglement entropy to classify three behaviors: thermalized, nonergodic extended, and localized. We also extract the localization length in the localized phase using the long-time dynamics of the entanglement entropy and the spin imbalance. Our work demonstrates the rich localization landscape of generalized Aubry-Andr\'e models containing mobility edges in contrast to the simple Aubry-Andr\'e model with no mobility edge.