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

TL;DR

This paper maps the non-equilibrium phase diagram of a generalized Aubry-Andre9-Harper model with a mobility edge, revealing unique transport properties and a connection to critical wavefunctions, using exact Green's function calculations.

Contribution

It introduces a detailed non-equilibrium phase diagram for the GAAH model, highlighting the distinct transport scaling at the mobility edge and its relation to the critical AAH model.

Findings

Critical line separates ballistic and localized transport regimes.

Current scales sub-diffusively with system size on the critical line.

Scaling exponent differs from that of the critical AAH model.

Abstract

We investigate and map out the non-equilibrium phase diagram of a generalization of the well known Aubry-Andr\'e-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 imbalance, we get hints of a rich phase diagram. We 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. Current is 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 critical point of AAH model, current scales sub-diffusively with system size on the 'critical' line ($I\sim N^{-2\pm0.1}$). However, remarkably, the scaling exponent on this line is distinctly different from that obtained for the critical AAH model (where $I\sim N^{-1.4\pm0.05}$). All these results can be understood from the above-mentioned connection between states near mobility edge of GAAH model and those of critical AAH model. A very interesting high temperature non-equilibrium phase diagram of the GAAH model emerges from our calculations.