Nonlinear sigma model approach for level correlations in chiral disordered systems

TL;DR

This paper develops a supersymmetric nonlinear sigma model for chiral disordered systems, deriving level correlation functions and density of states, and compares results with existing models, highlighting unique renormalization effects.

Contribution

It introduces a new sigma model approach for chiral systems and calculates spectral correlations, extending traditional nonchiral methods.

Findings

Derived a supersymmetric nonlinear sigma model for chiral systems.

Calculated density of states and two-level correlation functions.

Identified renormalization of mean level spacing in chiral systems.

Abstract

We study level correlations of disordered systems with chiral unitary symmetry (AIII symmetry). We use a random matrix model with a finite correlation length to derive a supersymmetric nonlinear sigma model. The result is compared with existing results based on other models. Using the methods by Kravtsov and Mirlin (Pis'ma Zh. Eksp. Teor. Fiz. 60, 645 (1994) [JETP Lett. 60, 656 (1994)]) and Andreev and Altshuler [Phys. Rev. Lett. 75, 902 (1995)], we calculate the density of states and two-level correlation function. The result is expressed using the spectral determinant as in traditional nonchiral systems. We discuss the renormalization of the mean level spacing which is not present in the traditional systems.