Localization spectrum of a bath-coupled generalized Aubry-Andr\'e model in the presence of interactions

Yi-Ting Tu, DinhDuy Vu, Sankar Das Sarma
Condensed Matter, Disordered Systems and Neural Networks, Disordered Systems and Neural Networks (cond-mat.dis-nn)
Phys. Rev. B 108, 064313 (2023)
2023-05-23 16:00:00
A generalization of the Aubry-Andr\'e model, the non-interacting GPD model introduced in S. 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 non-ergodic 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, non-ergodic 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.
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