Non-perturbative Solution of the Unitary, $N$-Orbital Anderson Model

TL;DR

This paper provides a non-perturbative analysis of the N-orbital Anderson model, identifying the mobility edge and the conditions for electron localization in a disordered system.

Contribution

It introduces a non-perturbative approach to analyze the N-orbital Anderson model, revealing the destabilization of diffusive behavior and deriving a localization criterion.

Findings

Mobility edge determined from non-perturbative analysis.

Replicon fluctuations destabilize diffusive regime.

Localization criterion expressed via a single scaling parameter.

Abstract

The mobility edge is extracted from a non-perturbative analysis of F. Wegner's real matrix ensemble (RME), $N$-orbital model of electrons with broken time-reversal invariance moving in random potential. The replicon fluctuations around the zero-dimensional (0D), single metallic grain saddlepoint, are shown to destabilize diffusive regime beyond the low energy limit yielding a precise criteria of localization in terms of a single scaling parameter.