Random matrices, symmetries, and many-body states

TL;DR

This paper investigates how random matrix models with symmetries can explain the prevalence of zero angular momentum ground states in nuclei, revealing broader many-body phenomena beyond pairing forces.

Contribution

It introduces a method to project random Hermitian matrices with good quantum numbers and analyzes ground state properties across different nuclear systems.

Findings

Ground states are dominated by low quantum numbers like J=0.

Odd-Z, odd-N systems with isospin conservation have fewer J=0 ground states.

Random matrix models can replicate observed nuclear ground state patterns.

Abstract

All nuclei with even numbers of protons and of neutrons have ground states with zero angular momentum. This is ascribed to the pairing force between nucleons, but simulations with random interactions suggest a much broader many-body phenomenon. In this Letter I project out random Hermitian matrices that have good quantum numbers and, computing the width of the Hamiltonian in subspaces, find ground states dominated by low quantum numbers, e.g. J=0. Furthermore I find odd-$Z$, odd-$N$ systems with isospin conservation have relatively fewer J=0 ground states.