Parametric invariant Random Matrix Model and the emergence of multifractality

TL;DR

This paper introduces a parametric invariant random matrix model inspired by chaotic systems, revealing a non-perturbative crossover to multifractality in eigenstates, advancing understanding of quantum chaos and eigenstate complexity.

Contribution

It presents a novel invariant random matrix model capturing parametric evolution and demonstrates a new crossover to multifractality in eigenstates.

Findings

Identification of a non-perturbative crossover to multifractality

Model exhibits parametric invariance with non-perturbative features

Insights into eigenstate complexity in chaotic quantum systems

Abstract

We propose a random matrix modeling for the parametric evolution of eigenstates. The model is inspired by a large class of quantized chaotic systems. Its unique feature is having parametric invariance while still possessing the non-perturbative crossover that has been discussed by Wigner 50 years ago. Of particular interest is the emergence of an additional crossover to multifractality.