Density of states for almost diagonal random matrices

TL;DR

This paper investigates the density of states in disordered systems modeled by almost diagonal Hermitian random matrices, providing analytical corrections to the Poissonian DOS for specific ensembles and models.

Contribution

It introduces a virial expansion method to compute leading corrections to the DOS in almost diagonal random matrices, extending analysis to various ensembles and models.

Findings

Derived correction formulas for Gaussian Orthogonal and Unitary Ensembles

Applied formulas to power-law banded and Moshe-Neuberger-Shapiro models

Compared DOS across different random matrix models

Abstract

We study the density of states (DOS) for disordered systems whose spectral statistics can be described by a Gaussian ensemble of almost diagonal Hermitian random matrices. The matrices have independent random entries $ H_{i \geq j} $ with small off-diagonal elements: $ <|H_{i \neq j}|^{2} > \ll <|H_{ii}|^{2} > \sim 1 $. Using the recently suggested method of a {\it virial expansion in the number of interacting energy levels} (Journ.Phys.A {\bf 36}, 8265), we calculate the leading correction to the Poissonian DOS in the cases of the Gaussian Orthogonal and Unitary Ensembles. We apply the general formula to the critical power-law banded random matrices and the unitary Moshe-Neuberger-Shapiro model and compare DOS of these models.