Level Correlations in Disordered Metals: the Replica sigma-Model

TL;DR

This paper calculates energy level correlations in disordered metals using the replica sigma-model, showing the importance of replica symmetry breaking saddle points to match known results across different ensembles.

Contribution

It demonstrates that including replica symmetry breaking saddle points in the fermionic replica sigma-model is essential for accurate energy level correlation calculations in disordered metals.

Findings

Results match supersymmetric sigma-model predictions.

Includes finite-dimensional gradient corrections.

Applicable to GOE, GUE, and GSE ensembles.

Abstract

We compute energy level correlations in weakly disordered metallic grains using the fermionic replica method. We use the standard sigma-model approach and show that non--trivial saddle points, which break replica symmetry, must be included in the calculation to reproduce the oscillatory behavior of the correlations. We calculate the correlation functions in all three classical ensembles GOE, GUE and GSE including the finite-dimensional gradient corrections. Our results coincides with those obtained by the supersymmetric sigma-model and the semi-classical trace formula.