Non-perturbative results for level correlations from the replica nonlinear sigma model

TL;DR

This paper demonstrates that the replica nonlinear sigma model accurately captures non-perturbative two-level correlation functions in disordered metals across all standard symmetry classes, aligning with known exact results in the large frequency limit.

Contribution

It shows that the replica nonlinear sigma model provides correct non-perturbative results for level correlations, including oscillatory contributions, for all three symmetry classes.

Findings

Replica sigma model yields correct R_2(ω) in large ω limit.

Non-perturbative oscillations from replica-symmetry breaking saddle points.

Results consistent with exact integral representations in the unitary case.

Abstract

We show that for all the three standard symmetry classes (unitary, orthogonal and symplectic), the conventional replica nonlinear sigma model gives the correct non-perturbative result for the two-level correlation functions R_2(\omega) of electrons in disordered metals in the limit of large \omega. In this limit, non-perturbative oscillatory contributions arise from a degenerate saddle-point manifold within this sigma model which corresponds to the replica-symmetry breaking. Moreover, we demonstrate that in the unitary case the very same results can be extracted from the well known exact integral representation for R_2(\omega).