Nonequilibrium phase diagram of a one-dimensional quasiperiodic system with a single-particle mobility edge

We investigate and map out the nonequilibrium 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 the AAH model. By calculating the population imbalance, we get hints of a rich phase diagram. We also find a fascinating connection between single particle wave functions near the mobility edge of the GAAH model and the wave functions 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 nonequilibrium steady state (NESS) current, calculated by fully exact nonequilibrium 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 the AAH model, current scales subdiffusively with system size on the 'critical' line (I similar to N-2 +/- 0.1). However, remarkably, the scaling exponent on this line is distinctly different from that obtained for the critical AAH model (where I similar to N-1.4 +/- 0.05). All these results can be understood from the above-mentioned connection between states near the mobility edge of the GAAH model and those of the critical AAH model. A very interesting high temperature nonequilibrium phase diagram of the GAAH model emerges from our calculations.