Anomalous localisation near the band centre in the 1D Anderson model: Hamiltonian map approach

TL;DR

This paper provides an analytical solution for the localization length near the band center in the 1D Anderson model with weak disorder, using the Hamiltonian map approach, supported by numerical data.

Contribution

It introduces a full analytical solution for localization length near the band center in the 1D Anderson model using the Hamiltonian map approach, outperforming previous methods.

Findings

Analytical expressions for localization length near band center.

Numerical data supporting the analytical results.

Implications for the single-parameter scaling hypothesis.

Abstract

We present a full analytical solution for the localisation length in the one-dimensional Anderson model with weak diagonal disorder in the vicinity of the band centre. The results are obtained with the Hamiltonian map approach that turns out to be more effective than other known methods. The analytical expressions are supported by numerical data. We also discuss the implications of our results for the single-parameter scaling hypothesis.