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

TL;DR

The island of inversion near $N=20$ challenges conventional shell-model pictures due to cross-shell intruder configurations. The authors apply ab initio VS-IMSRG calculations in the $sdpf$ model space to generate nuclear wavefunctions and analyze them with information-theoretic metrics, including proton–neutron entanglement entropy $S_{pn}$, mutual information, and quantum relative entropy $D_{KL}$ and $D_{JS}$. They show that $S_{pn}$ tracks cross-shell mixing and intruder content, mutual information reveals dominant like-particle correlations with proton–neutron correlations emerging in excited states and IoI regions, and mode-resolved quantum relative entropy identifies neutron orbitals driving state distinguishability between $0^+$ and $2^+$ states. Collectively, these measures provide a unified, quantitative view of how structural evolution around the IoI manifests in entanglement and correlation patterns, with implications for optimized quantum simulations of nuclear systems.

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.

Figures (13)

• Figure 1: Left panels: Configuration mixing for Ne, Mg, and Si isotopic chains, shown as the fractional contributions of normal (0p0h) and intruder (2p2h and 4p4h) configurations in the $sdpf$ model space for the lowest $0^+$, $2^+$, and $4^+$ states. Right panels: Corresponding proton-neutron entanglement entropy $S_{pn}$ for the same nuclei and states as a function of mass number. The vertical dashed lines indicate the position of the $N=20$ shell closure.
• Figure 2: Proton-neutron entanglement entropy $S_{pn}$ (upper panel) and corresponding configuration (lower panel) for the $N=20$ isotones from $^{29}$F to $^{35}$ P. The red bars correspond to the nuclei under the IoI. The configuration mixing is shown as the fractional contributions of normal (0p0h) and intruder (2p2h and 4p4h) configurations.
• Figure 3: We have illustrated the valence spaces considered for our calculations, consisting of the $sd$ shell for protons (blue) and the $sd$ and $pf$ shells for neutrons (red). The fully filled $^{16}$O core and the restricted $pf$ shell for protons are represented in grey. We have demonstrated one of the configurations of $^{32}$Mg.
• Figure 4: Mutual information for the first $0^+$ states of $^{24-34}$Ne in the $sdpf$ model space. Red (blue) arrows denote neutron (proton) orbitals, with magnetic substates ordered from $-j$ to $+j$. Solid lines separate the proton--proton, neutron--neutron, and proton--neutron sectors, while dashed lines indicate the boundaries between subshells. The off-diagonal solid blocks correspond to like-particle correlations, whereas the diagonal blocks represent proton--neutron correlations.
• Figure 5: Mutual information for the first $2^+$ states of $^{24-34}$Ne in the $sdpf$ model space. Same scheme as followed in Fig.\ref{['fig:Ne_MI_0+']}. The magnitude of the colorbar for the pn sectors differs from that of the $0^+$ states.