Smoothed universal correlations in the two-dimensional Anderson model

TL;DR

This paper investigates spectral correlations in the 2D Anderson model with weak disorder, comparing semiclassical analytical predictions to numerical results, and explores the effects of magnetic flux and time-reversal symmetry breaking.

Contribution

It provides a detailed semiclassical analysis of spectral correlations in the 2D Anderson model, including parametric correlations with magnetic flux, and compares these with numerical data.

Findings

Semiclassical and numerical correlation functions agree well near the mean level spacing.

Correlation functions depend on magnetic flux and symmetry breaking.

The analysis supports the universality predicted by random matrix theory.

Abstract

We report on calculations of smoothed spectral correlations in the two-dimensional Anderson model for weak disorder. As pointed out in (M. Wilkinson, J. Phys. A: Math. Gen. 21, 1173 (1988)), an analysis of the smoothing dependence of the correlation functions provides a sensitive means of establishing consistency with random matrix theory. We use a semiclassical approach to describe these fluctuations and offer a detailed comparison between numerical and analytical calculations for an exhaustive set of two-point correlation functions. We consider parametric correlation functions with an external Aharonov-Bohm flux as a parameter and discuss two cases, namely broken time-reversal invariance and partial breaking of time-reversal invariance. Three types of correlation functions are considered: density-of-states, velocity and matrix element correlation functions. For the values of smoothing parameter close to the mean level spacing the semiclassical expressions and the numerical results agree quite well in the whole range of the magnetic flux.