Random matrix ensembles with random interactions: Results for EGUE(2)-SU(4)

TL;DR

This paper introduces a new class of random matrix ensembles, EGUE(2)-SU(4), incorporating SU(4) symmetry relevant to nuclear physics, and analytically explores how symmetries influence spectral properties and chaos.

Contribution

The paper formulates and analyzes EGUE(2)-SU(4), a novel ensemble of random matrices with SU(4) symmetry, providing analytical formulas for covariances and insights into symmetry-induced chaos.

Findings

Covariances increase from EGUE(2) to EGUE(2)-SU(4)

Symmetries may induce chaos in finite quantum systems

Analytical formulas derived for spectral covariances

Abstract

We introduce in this paper embedded Gaussian unitary ensemble of random matrices, for $m$ fermions in $\Omega$ number of single particle orbits, generated by random two-body interactions that are SU(4) scalar, called EGUE(2)-SU(4). Here the SU(4) algebra corresponds to Wigner's supermultiplet SU(4) symmetry in nuclei. Formulation based on Wigner-Racah algebra of the embedding algebra $U(4\Omega) \supset U(\Omega) \otimes SU(4)$ allows for analytical treatment of this ensemble and using this analytical formulas are derived for the covariances in energy centroids and spectral variances. It is found that these covariances increase in magnitude as we go from EGUE(2) to EGUE(2)-$\cs$ to EGUE(2)-SU(4) implying that symmetries may be responsible for chaos in finite interacting quantum systems.