Localization in a strongly disordered system: A perturbation approach

TL;DR

This paper analytically proves localization in a strongly disordered 2D system with off-diagonal disorder, deriving a scaling law for the localization length that aligns with theoretical and numerical expectations.

Contribution

It introduces a perturbation approach to analytically determine localization length and critical exponents in a strongly disordered 2D Anderson model.

Findings

Localization length diverges at zero energy

Critical exponent ν=1 consistent with Chayes criterion

Analytical scaling law matches numerical results

Abstract

We prove that a strongly disordered two-dimensional system localizes with a localization length given analytically. We get a scaling law with a critical exponent is $\nu=1$ in agreement with the Chayes criterion $\nu\ge 1$. The case we are considering is for off-diagonal disorder. The method we use is a perturbation approach holding in the limit of an infinitely large perturbation as recently devised and the Anderson model is considered with a Gaussian distribution of disorder. The localization length diverges when energy goes to zero with a scaling law in agreement to numerical and theoretical expectations.