Anderson localization due to random magnetic field in two dimensions

TL;DR

This paper investigates Anderson localization in a 2D lattice with random magnetic flux, revealing critical behavior similar to known models and showing most states are localized except at zero energy.

Contribution

It provides large-scale numerical evidence that a 2D random flux model exhibits the same critical behavior as previously studied models, with detailed analysis of localization and density of states.

Findings

Most states are localized except at zero energy

Density of states has a singularity at the band center

Critical behavior matches that of Gade and Wegner's model

Abstract

Results of large-scale numerical simulations are reported on the Anderson localization in a two-dimensional square lattice tight-binding model with random flux. Localization lengths, fluctuations of the conductance, and the density of states are computed for quasi-one-dimensional geometry. Numerical results indicate that the model exhibits the same critical behavior as the one studied by Gade and Wegner. It is argued that all the states except a zero-energy state are localized and the density of states has a singularity in the center of the band. The energy scale below which the density of states increases is found to be extremely small.