Dynamical phases of interacting Andre-Aubry-Harper model

The dynamics of non-integrable quantum many-body systems have received extensive attention for both theoretical and practical purposes. One important issue we address in this talk is the phase transition between thermal and many-body-localized states and the dynamical properties of their possible intermediate states. We calculate the non-equilibrium steady states (NESS) of the boundary-driven strongly interacting Andre-Aubry-Harper model by employing the time-evolving block decimation on matrix product density operators. The spin and energy transport properties of the system are obtained from the NESS, which reveals a rich phase diagram while tuning the quasiperiodic potential strength. We uncover an exotic dynamical phase following the thermal phase where the spin transport becomes sub-diffusive while the butterfly velocity remains non-zero, and also investigate the entanglement properties of each phase.