Localization transitions and mobility edges in coupled Aubry-Andre chains

We study the localization transitions for coupled one-dimensional lattices with quasiperiodic potential. In addition to the localized and extended phases, there is an intermediate mixed phase that can be easily explained decoupling the system so as to deal with effective uncoupled Aubry-Andre 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 that compose an extension of the Aubry-Andre 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-Andre model, with quasiperiodic potentials in any directions, and the 2D Anderson model.