Exponents of the localization length in the 2D Anderson model with off-diagonal disorder

TL;DR

This paper investigates the divergence of localization lengths in 2D Anderson models with off-diagonal disorder, revealing detailed scaling behaviors and divergence exponents near the band center.

Contribution

It provides a detailed numerical analysis of localization length divergence in 2D off-diagonal disordered systems, including bipartite and non-bipartite lattices, with new divergence exponents.

Findings

Localization lengths diverge near the band center with well-described power laws.

Divergence exponents effectively model the data down to very small scales (~10^-5).

Little evidence found for a crossover energy scale where the power law fails.

Abstract

We study Anderson localization in two-dimensional systems with purely off-diagonal disorder. Localization lengths are computed by the transfer-matrix method and their finite-size and scaling properties are investigated. We find various numerically challenging differences to the usual problems with diagonal disorder. In particular, the divergence of the localization lengths close to the band centre is investigated in detail for bipartite and non-bipartite lattices as well as different distributions of the off-diagonal disorder. Divergence exponents for the localization lengths are constructed that appear to describe the data well down to at least 10^-5. We find only little evidence for a crossover energy scale below which the power law has been argued to fail.