Entanglement and seniority

TL;DR

This paper analyzes mode-entanglement within the seniority nuclear model, deriving formulas, performing numerical calculations on isotopes, and comparing predictions with advanced computational methods to understand entanglement and seniority mixing effects.

Contribution

It provides analytic formulas for reduced density matrices at various seniority levels and compares seniority model predictions with CI and DMRG results for nuclear isotopes.

Findings

Seniority model explains mode entropies in $^{94}$Ru.

Seniority mixing affects yrast states significantly.

Interaction induces quantum fluctuations reducing shell occupations.

Abstract

We study mode-entanglement in the seniority model, derive analytic formulas for the one-body reduced density matrix of states with seniority $\nu = 0,\;1,\;2$, and $\nu=3$, and also determine the particle number dependence of the one-body reduced density matrix for arbitrary seniority. We carry out numerical calculations for the lightest calcium isotopes and for $^{94}{\rm Ru}$ nucleus, and investigate the structure of their ground and low energy yrast states. We investigate the fulfillment of several predictions of the seniority model regarding the behavior of one-mode entropies, which we compare with the results of configuration interaction (CI) and density matrix renormalization group (DMRG) computations. For $^{94}{\rm Ru}$, the seniority model accounts for the $0g_{9/2}$ mode entropies, but seniority mixing is important for certain yrast states. Interaction induced quantum fluctuations decrease the occupation of the $0f_{5/2}$, $1p_{3/2}$ and $1p_{1/2}$ shells, and amount in finite mode entropies on these shells, too, clearly outside the scope of the simple $(0g_{9/2})^4$ seniority model. The $0f_{7/2}$ shell based seniority model is more accurate for the light ${\rm Ca}$ isotopes, but seniority mixing is substantial for some $^{44}{\rm Ca}$ yrast states, too.