Universal and non-universal features of the multifractality exponents of critical wave-functions

TL;DR

This paper investigates the multifractality spectrum of critical wave-functions in random matrix ensembles, revealing universal behavior at leading order and model-specific features at higher orders.

Contribution

It provides a perturbative analysis of the multifractality spectrum, distinguishing universal and non-universal features across different random matrix models.

Findings

Leading order spectrum is universal across models.

Higher order corrections are model-specific.

Explicit anomalous dimensions derived for specific ensembles.

Abstract

We calculate perturbatively the multifractality spectrum of wave-functions in critical random matrix ensembles in the regime of weak multifractality. We show that in the leading order the spectrum is universal, while the higher order corrections are model-specific. Explicit results for the anomalous dimensions are derived in the power-law and ultrametric random matrix ensembles.