Non-local corrections to the typical medium theory of Anderson localization

TL;DR

This paper introduces a finite cluster typical medium approach to better understand Anderson localization in three dimensions, emphasizing the role of non-local correlations and environment effects in accurately characterizing the transition.

Contribution

The study develops a systematic cluster-based method that incorporates non-local correlations, improving the accuracy of localization transition predictions compared to previous models.

Findings

Converges quickly with cluster size

Recovers correct critical disorder strength

Highlights importance of non-local correlations

Abstract

We use the recently developed finite cluster typical medium approach to study the Anderson localization transition in three dimensions. Applying our method to the box and binary alloy disorder distributions, we find a fast convergence with the cluster size. We demonstrate the importance of the typical medium environment and the non-local spatial correlations for the proper characterization of the localization transition. As the cluster size increases, our typical medium cluster method recovers the correct critical disorder strength for the transition. Our findings highlight the importance of the non-local cluster corrections for capturing the localization behavior of the mobility edge trajectories. Our results demonstrate that the typical medium cluster approach developed here provides a consistent and systematic description of the Anderson localization transition in the framework of the effective medium embedding schemes.