Localization length in a random magnetic field

TL;DR

This paper investigates the localization length in a two-dimensional lattice with random magnetic fluxes using the Kubo formula, revealing how conductance decay relates to localization in disordered quantum systems.

Contribution

It introduces a numerical method to compute localization length in a non-diagonal disorder model with random magnetic fluxes, extending standard Anderson localization results.

Findings

Localization length remains below 10,000 units in the main band

Exponential increase of localization length near band edges

Standard Anderson model results are recovered in specific cases

Abstract

Kubo formula is used to get the d.c conductance of a statistical ensemble of two dimensional clusters of the square lattice in the presence of random magnetic fluxes. Fluxes traversing lattice plaquettes are distributed uniformly between minus one half and plus one half of the flux quantum. The localization length is obtained from the exponential decay of the averaged conductance as a function of the cluster side. Standard results are recovered when this numerical approach is applied to Anderson model of diagonal disorder. The localization length of the complex non-diagonal model of disorder remains well below 10 000 (in units of the lattice constant) in the main part of the band in spite of its exponential increase near the band edges.