Entanglement and seniority

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.