Zero Energy anomaly in one-dimensional Anderson lattice with exponentially correlated weak diadonal disorder

TL;DR

This paper investigates how correlated diagonal disorder affects the localization length at zero energy in a one-dimensional Anderson model, revealing the importance of higher order terms for accurate predictions.

Contribution

It introduces a numerical analysis of the localization length considering correlated disorder and highlights the necessity of higher order terms in perturbation theory.

Findings

Localization length varies continuously with disorder correlation.

Higher order correlation terms are essential for accurate localization length.

The study connects zero correlation anomaly with large correlation perturbation results.

Abstract

We calculated numerically the localization length of one-dimensional Anderson model with correlated diagonal disorder. For zero energy point in the weak disorder limit, we showed that the localization length changes continuously as the correlation of the disorder increases. We found that higher order terms of the correlation must be included into the current perturbation result in order to give the correct localization length, and to connect smoothly the anomaly at zero correlation with the perturbation result for large correlation.