New Class of Random Matrix Ensembles with Multifractal Eigenvectors

TL;DR

This paper introduces a new class of critical random matrix ensembles characterized by multifractal eigenvectors, linking three models through an exact mapping and discussing their universal spectral statistics relevant to Anderson transitions and chaotic systems.

Contribution

It establishes a unified framework for three random matrix ensembles with multifractal eigenvectors, proposing their classification as a new critical ensemble with universal spectral properties.

Findings

Eigenvector statistics are multifractal in these ensembles.

A universal form of the two-level correlation function is proposed.

Applications include spectral analysis at the Anderson transition.

Abstract

Three recently suggested random matrix ensembles (RME) are linked together by an exact mapping and plausible conjections. Since it is known that in one of these ensembles the eigenvector statistics is multifractal, we argue that all three ensembles belong to a new class of critical RME with multifractal eigenfunction statistics and a universal critical spectral statitics. The generic form of the two-level correlation function for weak and extremely strong multifractality is suggested. Applications to the spectral statistics at the Anderson transition and for certain systems on the border of chaos and integrability is discussed.