Supersymmetry for disordered systems with interaction

TL;DR

This paper introduces a supersymmetric sigma-model for disordered electron systems with interactions, simplifying calculations and enabling potential non-perturbative analysis, especially for weak short-range interactions.

Contribution

It develops a supersymmetric approach to include electron-electron interactions in disordered systems, providing a new tool for theoretical analysis.

Findings

Model reproduces known renormalization group equations

Simplifies averaging over disorder

Potential for non-perturbative calculations

Abstract

Considering disordered electron systems we suggest a scheme that allows us to include an electron-electron interaction into a supermatrix sigma-model. The method is based on replacing the initial model of interacting electons by a fully supersymmetric model. Although this replacement is not exact, it is a good approximation for a weak short range interaction and arbitrary disorder. The replacement makes the averaging over disorder and further manipulations straightforward and we come to a supermatrix sigma-model containing an interaction term. The structure of the model is rather similar to the replica one, although the interaction term has a different form. We study the model making perturbation theory and renormalization group calculations. We check the renormalizability of the model in the first loop approximation and in the first order in the interaction. In this limit we reproduce the renormalization group equations known from earlier works. We hope that the new supermatrix sigma-model may become a new tool for non-perturbative calculations for disordered systems with interaction.