Energy level statistics of a critical random matrix ensemble

TL;DR

This paper investigates the spectral statistics of a critical random matrix ensemble with power-law banded matrices, combining numerical computations with analytical comparisons to understand level compressibility.

Contribution

It introduces a detailed numerical analysis of level statistics in a critical random matrix ensemble and compares results with an existing analytical model.

Findings

Numerical results for level compressibility match the analytical formula.

The study confirms the critical nature of the spectral statistics.

Provides insights into the universality of level fluctuations in critical ensembles.

Abstract

We study level statistics of a critical random matrix ensemble of a power-law banded complex Hermitean matrices. We compute numerically the level compressibility via the level number variance and compare it with the analytical formula for the exactly solvable model of Moshe, Neuberger and Shapiro.