Mobility Edges in one-dimensional Models with quasi-periodic disorder

TL;DR

This paper introduces an efficient method to determine mobility edges in one-dimensional quasi-periodic disordered models by approximating them with periodic models and analyzing their energy band overlaps.

Contribution

It presents a novel approximation technique for identifying mobility edges and proposes an index to quantify eigenstate localization in quasi-periodic models.

Findings

Mobility edges can be accurately located using band overlap analysis.

The proposed index effectively indicates the degree of localization.

The method simplifies the analysis of complex quasi-periodic systems.

Abstract

We study the mobility edges in a variety of one-dimensional tight binding models with slowly varying quasi-periodic disorders. It is found that the quasi-periodic disordered models can be approximated by an ensemble of periodic models. The mobility edges can be determined by the overlaps of the energy bands of these periodic models. We demonstrate that this method provides an efficient way to find out the precise location of mobility edge in qusi-periodic disordered models. Based on this approximate method, we also propose an index to indicate the degree of localization of each eigenstate.