Localization-delocalization transition in a one-dimensional system with long-range correlated off-diagonal disorder

TL;DR

This paper investigates how long-range correlations in off-diagonal disorder influence electron localization in a one-dimensional system, revealing a transition point at a critical Hurst exponent and providing analytical and numerical insights.

Contribution

It introduces an analytical expression for localization length considering correlations and identifies a localization-delocalization transition at a specific Hurst exponent.

Findings

Localization-delocalization transition at H=1/2 for correlated disorder

Analytical expression for localization length at the band center

Finite size scaling relations for localization length near the band center

Abstract

The localization behavior of the one-dimensional Anderson model with correlated and uncorrelated purely off-diagonal disorder is studied. Using the transfer matrix method, we derive an analytical expression for the localization length at the band center in terms of the pair correlation function. It is proved that for long-range correlated hopping disorder, a localization-delocalization transition occurs at the critical Hurst exponent H_c= 1/2 when the variance of the logarithm of hopping "\sigma_{\ln(t)}" is kept fixed with the system size N. Based on numerical calculations, finite size scaling relations are postulated for the localization length near the band center (E \neq 0) in terms of the system parameters: E,N,H, and \sigma_{\ln(t)}.