Non-equilibrium phase diagram of a 1D quasiperiodic system with a single-particle mobility edge

We investigate and map out the non-equilibrium phase diagram of a generalization of the well known Aubry-Andre-Harper (AAH) model. This generalized AAH (GAAH) model is known to have a single-particle mobility edge which also has an additional self-dual property akin to that of the critical point of AAH model. By calculating the population imbalance, we get hints of a rich phase diagram. We also find a fascinating connection between single particle wavefunctions near the mobility edge of GAAH model and the wavefunctions of the critical AAH model. By placing this model far-from-equilibrium with the aid of two baths, we investigate the open system transport via system size scaling of non-equilibrium steady state (NESS) current, calculated by fully exact non-equilibrium Green's function (NEGF) formalism. The critical point of the AAH model now generalizes to a `critical' line separating regions of ballistic and localized transport. Like the critical point of AAH model, current scales sub-diffusively with system size on the `critical' line. However, remarkably, the scaling exponent on this line is distinctly different from that obtained for the critical AAH model. A very interesting high temperature non-equilibrium phase diagram of the GAAH model emerges from our calculations.