Entanglement study in the island of inversion region using \textit{ab initio} approach

TL;DR

This study uses quantum entanglement measures within an extit{ab initio} framework to analyze nuclear structure and correlations near the neutron-rich island of inversion, revealing insights into entanglement patterns and their role in nuclear phenomena.

Contribution

It introduces a comprehensive entanglement analysis using advanced measures in extit{ab initio} nuclear calculations to understand the island of inversion region.

Findings

Proton-neutron entanglement entropy highlights the formation of the island of inversion.

Mutual information reveals correlation strengths between nucleon states, increasing in excited states.

Quantum relative entropy distinguishes differences between nuclear states using divergence measures.

Abstract

Quantum entanglement provides a unique perspective for probing nuclear structure. In this work, we employ quantum entanglement measures, including proton-neutron entanglement entropy, mutual information, and quantum relative entropy, to investigate the evolution of entanglement patterns as we approach neutron-rich nuclei. The study is carried out in the vicinity of the $N=20$ island of inversion region consisting of even-$A$ Ne, Mg, and Si isotopes, and also for isotones corresponding to $N=20$. The state-of-the-art \textit{ab initio} valence space in-medium similarity renormalization group method has been used for this purpose. We have highlighted the role of proton-neutron entanglement entropy in the formation of the island of inversion region. Mutual information provides insight into the strength of correlations between proton-proton, neutron-neutron, and proton-neutron single-particle states. While these correlations are relatively weak between protons and neutrons in the ground states, they become comparable to like-particle correlations in excited states. The quantum relative entropy is also studied between $0^+$ and $2^+$ states of the Ne, Mg, and Si isotopes, as well as $N=20$ isotones, using the Kullback-Leibler divergence and Jensen-Shannon divergence. We have performed these calculations by expressing the nuclear wavefunctions in a Slater-determinant basis and analyzing them through complementary partitions, including proton-neutron and mode-resolved factorizations.