Mobility edges in one dimensional models with large quasi-periodic disorders

TL;DR

This paper investigates one-dimensional models with large quasi-periodic disorders and demonstrates that such models can support mobility edges, similar to slowly varying disorders, confirmed through analytical and numerical methods.

Contribution

It introduces the concept that large quasi-periodic disorders can support mobility edges, expanding understanding of localization phenomena in 1D systems.

Findings

Large quasi-periodic disorders support mobility edges.

Energy matching method effectively locates mobility edges.

Numerical calculations verify the analytical predictions.

Abstract

We study the one-dimensional tight-binding model with quasi-periodic disorders, where the quasi-period is tuned to be very large. It is found that this type of model with large quasi-periodic disorders can also support the mobility edges, which is very similar to the models with slowly varying quasi-periodic disorders. The energy matching method is employed to determine the locations of mobility edges in both types of models. These results of mobility edges are verified by numerical calculations in various examples. We also provide a qualitative arguments to support the fact that large quasi-periodic disorders will lead to the existence of mobility edges.