Localization transitions and mobility edges in coupled Aubry-André chains

M. Rossignolo, L. Dell'Anna

Published 2018-04-09, updated 2018-09-11Version 2

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 energy shift which compose a 2D Aubry-Andr\'e model. We study the localization behavior in this case comparing the results with those obtained for the 2D Anderson model.