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

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. While mutual information provides insight into the strong correlations between proton-proton and neutron-neutron single-particle orbitals. The correlations are weak between proton and neutron for ground states, but become comparable to like-particle correlations for 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 using partitions based on proton-neutron, single-particle states, and Slater determinants.