Unified description of perturbation theory and band center anomaly in one-dimensional Anderson localization

TL;DR

This paper numerically investigates the localization length in a one-dimensional Anderson model, unifying perturbation theory and band center anomaly descriptions through a single equation.

Contribution

It introduces a unified equation that describes localization length across different energies and disorder strengths, bridging perturbation theory and anomaly analysis.

Findings

Localization length varies continuously from band center to edge.

All localization lengths collapse onto a single curve for various parameters.

A simple equation fits the localization length data across conditions.

Abstract

We calculated numerically the localization length of one-dimensional Anderson model with diagonal disorder. For weak disorder, we showed that the localization length changes continuously as the energy changes from the band center to the boundary of the anomalous region near the band edge. We found that all the localization lengths for different disorder strengths and different energies collapse onto a single curve, which can be fitted by a simple equation. Thus the description of the perturbation theory and the band center anomaly were unified into this equation.