Localization transitions and mobility edges in coupled Aubry-Andr\'e chains

TL;DR

This paper investigates localization transitions and mobility edges in coupled Aubry-André chains, revealing an intermediate phase and conditions for a unique mobility edge, with extensions to two-dimensional systems and comparisons to other models.

Contribution

It introduces a detailed analysis of localization phases in coupled Aubry-André chains, identifying conditions for a unique mobility edge and extending the study to 2D systems.

Findings

Identification of an intermediate mixed phase in coupled chains.

Conditions for a uniquely defined mobility edge.

Comparison of localization behavior with 2D Aubry-André and Anderson models.

Abstract

We study the localization transitions for coupled one-dimensional lattices with quasiperiodic potential. Besides the localized and extended phases there is an intermediate mixed phase which can be easily explained decoupling the system so as to deal with effective uncoupled Aubry-Andr\'e chains with different transition points. We clarify, therefore, the origin of such an intermediate phase finding the conditions for getting a uniquely defined mobility edge for such coupled systems. Finally we consider many coupled chains with an energy shift which compose an extension of the Aubry-Andr\'e model in two dimensions. We study the localization behavior in this case comparing the results with those obtained for a truly aperiodic two-dimensional (2D) Aubry-Andr\'e model, with quasiperiodic potentials in any directions, and for the 2D Anderson model.