Long range disorder and Anderson transition in systems with chiral symmetry

2004/03/31 by Antonio M. Garcı́a-Garcı́a, Antonio M. Garcia-Garcia, Kazutaka Takahashi · 1 citation
Mathematics · Physics and Astronomy · #Quantum chaos and dynamical systems #Quantum many-body systems #Random Matrices and Applications #cond-mat.dis-nn #hep-th

paper · pdf · doi:10.1016/j.nuclphysb.2004.08.035

published as Nucl.Phys. B700 (2004) 361 · 17 pages, 4 figures; discussions on superconductivity removed

arxiv created 2004/09/14 · openalex publication_date 2004/09/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the spectral properties of a chiral random banded matrix (chRBM) with elements decaying as a power-law \cal H_ij∼ |i-j|^-α. This model is equivalent to a chiral 1D Anderson Hamiltonian with long range power-law hopping. In the weak disorder limit we obtain explicit nonperturbative analytical results for the density of states and the two-level correlation function by mapping the chRBM onto a nonlinear sigma model. We also put forward, by exploiting the relation between the chRBM at α=1 and a generalized chiral random matrix model, an exact expression for the above correlation functions. We give compelling analytical and numerical evidence that for this value the chRBM reproduces all the features of an Anderson transition. Finally we discuss possible applications of our results to QCD.

Cited by

• Boundary multifractality in critical one-dimensional systems with long-range hopping

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