Scaling properties of one-dimensional off-diagonal disorder

TL;DR

This paper investigates the validity of single parameter scaling in a one-dimensional Anderson model with off-diagonal disorder, revealing two regimes with different scaling behaviors and introducing a new length scale related to density of states.

Contribution

It identifies the existence of SPS and non-SPS regimes in off-diagonal disorder and proposes specific scaling relations for the Lyapunov Exponent in these regimes.

Findings

Localized region divided into SPS and non-SPS regimes

Introduction of a new length scale related to the density of states

Physical interpretation as a crossover length separating symmetry regions

Abstract

Validity of the single parameter scaling (SPS) in one dimensional Anderson model with purely off-diagonal disorder is being studied. It is shown that the localized region with standard symmetry is divided into two regimes: SPS and non-SPS. Scaling relations of the Lyapunov Exponent are proposed for these two regimes. In the non-SPS regime, in additional to the localization length, there exists a new length scale which is related to the integrated density of states. A physical interpretation of the new length is the cross-over length which separates regions with chiral symmetry from those that have standard symmetry.