Nonlocally-correlated disorder and delocalization in one dimension II: Localization length

TL;DR

This paper investigates how the localization length in a one-dimensional disordered system depends on the correlation length of the disorder, using supersymmetric methods, and confirms the findings with numerical studies.

Contribution

It introduces a calculation of the mean localization length in a disordered fermion system using supersymmetric techniques, highlighting the effect of disorder correlation.

Findings

Localization length increases with disorder correlation length.

Results agree with previous density of states calculations.

Numerical studies support the analytical findings.

Abstract

In the previous paper (cond-mat/9809323), we calculated the density of staes in the random-mass Dirac fermion system. In this paper, we obtain the mean localization length of the single-fermion Greem's function by using the supersymmetric methods. It is shown that the localization length is a increasing function of the correation length of the disorders. This result is in agreement with the density of states and the numerical studies (cond-mat/9903389).