Classical Representation of the 1D Anderson Model

TL;DR

This paper introduces a novel two-dimensional Hamiltonian map approach to analyze the 1D Anderson model, providing accurate localization length expressions at various energy band points, surpassing standard perturbation methods.

Contribution

It presents a new analytical method using a 2D Hamiltonian map for the 1D Anderson model, improving localization length calculations especially at band edges and for strong disorder.

Findings

Accurate localization length expressions at band center and edge for weak disorder.

Approximate analytical expressions for strong disorder.

Method surpasses standard perturbation theory in accuracy.

Abstract

A new approach is applied to the 1D Anderson model by making use of a two-dimensional Hamiltonian map. For a weak disorder this approach allows for a simple derivation of correct expressions for the localization length both at the center and at the edge of the energy band, where standard perturbation theory fails. Approximate analytical expressions for strong disorder are also obtained.