Nonlinearσmodel approach for level correlations in chiral disordered systems

2004/03/31 by Kazutaka Takahashi
Chemistry · Physics and Astronomy · #Molecular spectroscopy and chirality #Quantum chaos and dynamical systems #Spectroscopy and Quantum Chemical Studies #cond-mat.dis-nn #cond-mat.mes-hall

paper · pdf · doi:10.1103/physreve.70.066147

published as Phys.Rev. E70 (2004) 066147 · 21 pages, no figures; substantially revised and expanded; minor changes

arxiv created 2004/12/09 · openalex publication_date 2004/12/30 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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 of Sov. Phys. JETP 60, 656 (1994)] and 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.

Related

• Long range disorder and Anderson transition in systems with chiral symmetry
• Nonlinear Sigma Model for Disordered Media: Replica Trick for Non-Perturbative Results and Interactions
• Chiral Random Matrix Models: A Novel Intermediate Asymptotic Regime
• Non-linear sigma models for non-Hermitian random matrices in symmetry classes AI^† and AII^†
• Phase transition in the Integrated Density of States of the Anderson model arising from a supersymmetric sigma model