Parametrized Version of the Generalized Aubry-Andr\'e Model

TL;DR

This paper introduces a parametrized version of the generalized Aubry-Andre model, enabling simple solution characterization based on system energy, initial site, and a tuning parameter, enhancing understanding of localization phenomena.

Contribution

It develops a new parametrization of the generalized Aubry-Andre model using a recurrence-relation ansatz, linking solutions to three key parameters.

Findings

The model allows for easy identification of localized or extended states.

The standard Aubry-Andre model is recovered at alpha=0.

The parametrization simplifies analysis of quasiperiodic systems.

Abstract

A recently introduced recurrence-relation ansatz applied to the Bose-Hubbard model is here used in the generalized Aubry-Andre model. The resulting modified Aubry-Andre model allows for a simple parametrization of the solutions in terms of three parameters, viz., the system energy when the quasiperiodicity amplitude Delta = 0, the site mu where the particle is initially localized, and the tuning parameter -1 < alpha < 1 that determines the regions of localized or extended states. The standard Aubry-Andre form corresponds to alpha = 0.