Divergences of the localization lengths in the two- dimensional, off-diagonal Anderson model on bipartite lattices

TL;DR

This paper studies how localization lengths behave in a 2D off-diagonal Anderson model on bipartite lattices, revealing power-law divergence at small energies with exponents influenced by disorder type and strength.

Contribution

It provides a detailed analysis of localization length divergences in 2D off-diagonal Anderson models across various bipartite lattices and disorder distributions.

Findings

Localization lengths diverge as a power-law at small energies.

Exponents of divergence range from 0.2 to 0.6.

Divergence exponents depend on disorder type and strength.

Abstract

We investigate the scaling properties of the two-dimensional (2D) Anderson model of localization with purely off-diagonal disorder (random hopping). Using the transfer-matrix method and finite-size scaling we compute the infinite-size localization lengths for bipartite square and hexagonal 2D lattices, non-bipartite triangular lattices and different distribution functions for the hopping elements. We show that for small energies the localization lengths in the bipartite case diverge with a power-law behavior. The corresponding exponents are in the range $0.2 - 0.6$ and seem to depend on the type and the strength of disorder.