The band-centre anomaly in the 1D Anderson model with correlated disorder

TL;DR

This paper investigates how correlations in weak disorder affect the band-centre anomaly in the 1D Anderson model, providing analytical expressions for localization length and phase invariant measure.

Contribution

It offers new analytical insights into the impact of disorder correlations on the band-centre anomaly in the 1D Anderson model.

Findings

Correlations can enhance the anomaly.

Correlations can suppress the anomaly.

Analytical expressions for localization length and phase measure.

Abstract

We study the band-centre anomaly in the one-dimensional Anderson model with weak correlated disorder. Our analysis is based on the Hamiltonian map approach; the correspondence between the discrete model and its continuous counterpart is discussed in detail. We obtain analytical expressions of the localisation length and of the invariant measure of the phase variable, valid for energies in a neighbourhood of the band centre. By applying these general results to specific forms of correlated disorder, we show how correlations can enhance or suppress the anomaly at the band centre.