Non-equilibrium steady state phases of the interacting Aubry-Andre-Harper model

TL;DR

This paper explores the phase diagram of the interacting Aubry-Andre-Harper model, revealing complex dynamical phases characterized by unusual spin transport and correlations, distinct from traditional thermal and localized phases.

Contribution

It provides the first detailed analysis of non-equilibrium steady states in the strongly interacting Aubry-Andre-Harper model, highlighting multiple dynamical phases and transport behaviors.

Findings

Spin transport transitions from superdiffusive to subdiffusive before localization

Transport transition is distinct from operator growth transition

Unusual oscillation patterns in quantum correlations at intermediate potential strengths

Abstract

Here we study the phase diagram of the Aubry-Andre-Harper model in the presence of strong interactions as the strength of the quasiperiodic potential is varied. Previous work has established the existence of many-body localized phase at large potential strength; here, we find a rich phase diagram in the delocalized regime characterized by spin transport and unusual correlations. We calculate the non-equilibrium steady states of a boundary-driven strongly interacting Aubry-Andre-Harper model by employing the time-evolving block decimation algorithm on matrix product density operators. From these steady states, we extract spin transport as a function of system size and quasiperiodic potential strength. This data shows spin transport going from superdiffusive to subdiffusive well before the localization transition; comparing to previous results, we also find that the transport transition is distinct from a transition observed in the speed of operator growth in the model. We also investigate the correlation structure of the steady state and find an unusual oscillation pattern for intermediate values of the potential strength. The unusual spin transport and quantum correlation structure suggest multiple dynamical phases between the much-studied thermal and many-body-localized phases.