Random matrix theory for CPA: Generalization of Wegner's $n$--orbital model

TL;DR

This paper extends Wegner's $n$-orbital model for disordered systems by using randomly rotated matrices, providing exact solutions for Green's functions and conductivity in the large $n$ limit, and unifying various disorder models.

Contribution

It introduces a generalized ensemble of random matrices for the $n$-orbital model, enabling exact calculations and encompassing the Lloyd model within a unified framework.

Findings

Exact solutions for Green's functions and conductivity in the large $n$ limit.

The generalized model solves the CPA-equation for arbitrary disorder distributions.

The Lloyd model is shown to be a special case of the new framework.

Abstract

We introduce a generalization of Wegner's $n$-orbital model for the description of randomly disordered systems by replacing his ensemble of Gaussian random matrices by an ensemble of randomly rotated matrices. We calculate the one- and two-particle Green's functions and the conductivity exactly in the limit $n\to\infty$. Our solution solves the CPA-equation of the $(n=1)$-Anderson model for arbitrarily distributed disorder. We show how the Lloyd model is included in our model.