Statistical properties of the critical eigenstates in power-law random banded matrices across the band

TL;DR

This study numerically investigates the level-spacing distribution in the eigenvalue tails of power-law random banded matrices, revealing how spectral statistics vary across the band and with coupling strength.

Contribution

It demonstrates that level-spacing statistics can be controlled by eigenvalue regions, paralleling changes caused by coupling strength variations in PRBM ensembles.

Findings

Level-spacing distribution varies across the eigenvalue band.

Spectral statistics can be tuned by eigenvalue region or coupling strength.

Confirmed equivalence of spectral statistics through different parameter variations.

Abstract

The level-spacing distribution in the tails of the eigenvalue bands of the power-law random banded matrix (PRBM) ensemble have been investigated numerically. The change of level-spacing statistics across the band is examined for different coupling strengths and compared to the density of states for the different systems. It is confirmed that, by varying the eigenvalue region, the same level-spacing statistics can be reached as by varying the coupling strength.