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arXiv:2411.01861

Investigation of entanglement in $N = Z$ nuclei within no-core shell model

Chandan Sarma, P. C. Srivastava

Published Nov 4, 2024• 0 citations
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Abstract

In this work, we explore the entanglement structure of two $N = Z$ nuclei, $^{20}$Ne and $^{22}$Na using single-orbital entanglement entropy within the No-Core Shell Model (NCSM) framework for two realistic interactions, INOY and N$^3$LO. We begin with the determination of the optimal frequencies based on the variation of ground-state (g.s.) binding energy with NCSM parameters, $N_{max}$ and $\hbar Ω$, followed by an analysis of the total single-orbital entanglement entropy, $S_{tot}$, for the g.s. of $^{20}$Ne and $^{22}$Na. Our results show that $S_{tot}$ increases with $N_{max}$ and decreases with $\hbar Ω$ after reaching a maximum. We use $S_{tot}$ to guide the selection of an additional set of optimal frequencies that can enhance electromagnetic transition strengths. We also calculate the low-energy spectra and $S_{tot}$ for four low-lying states of $^{20}$Ne and six low-lying states of $^{22}$Na. Finally, we calculate a few $E2$ and one $M1$ transition strengths, finding that N$^3$LO provides better results for $B(E2; 5^+_1 \to 3^+_1$) and INOY performs well for the $B(M1; 0_1^+ \to 1_1^+)$ transition in the $^{22}$Na nucleus while considering the first set of optimal frequencies. We also observe that the second set of optimal frequencies enhances electromagnetic transition strengths, particularly for the states with large and comparable $S_{tot}$. Also, for both nuclei, the $S_{tot}$ for INOY and N$^3$LO are close while considering the second set of optimal frequencies, suggesting that the calculated $S_{tot}$ are more dependent on $\hbar Ω$ than the interactions employed for the same model space defined by the $N_{max}$ parameter.

DOI
10.48550/arxiv.2411.01861

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Background: One of the fundamental problems of quantum information science is quantum entanglement. Recently, quantum phase transition in nuclear systems is studied in connection with quantum entanglement.Purpose: In this paper, the use of entanglement entropy as a suitable signal for the study of quantum phase transition in the even-even and odd-AAA nuclei is investigated. The effect of the coupling of a single fermion to a boson core on entanglement entropy is studied.Method: By use of the affine SU(1,1)SU(1,1)SU(1,1) Lie algebra and through the Schmidt decomposition in the framework of the interacting boson model (IBM) and interacting boson-fermion model (IBFM), entanglement entropy in the even-even and odd-AAA are obtained. The entanglement entropy is used for tracking and studying the shape phase transition in these nuclei.Results: The entanglement entropy in the IBM and the IBFM is calculated. The entanglement entropy values of the low-lying states of 122−−134Xe,102−−110Pd^{122--134}\mathrm{Xe}, ^{102--110}\mathrm{Pd}122−−134Xe,102−−110Pd, and 123−−133Xe^{123--133}\mathrm{Xe}123−−133Xe were calculated and analyzed. It is found that entanglement entropy is a suitable order parameter to detect shape phase transition in nuclear systems.Conclusions: The obtained results indicate that the entropy of entanglement is sensitive to the shape-phase transition between spherical and $\ensuremath{\gamma}$-unstable regions in nuclei. The results show that entanglement entropy is a powerful tool for identifying shape phase transitions in nuclei. It is found that the coupling of the single fermion with angular momentum jjj to the even-even system does not change the geometry imposed by the boson core performing the transition and only the entanglement entropy values have been shifted by the addition of the odd particle with respect to the even case.
Abstract Quantum entanglement offers a unique perspective into the underlying structure of strongly-correlated systems such as atomic nuclei. In this paper, we use quantum information tools to analyze the structure of light and medium-mass berillyum, oxygen, neon and calcium isotopes within the nuclear shell model. We use different entanglement metrics, including single-orbital entanglement, mutual information, and von Neumann entropies for different equipartitions of the shell-model valence space and identify mode-entanglement patterns related to the energy, angular momentum and isospin of the nuclear single-particle orbitals. We observe that the single-orbital entanglement is directly related to the number of valence nucleons and the energy structure of the shell, while the mutual information highlights signatures of proton–proton and neutron–neutron pairing, as well as nuclear deformation. Proton and neutron orbitals are weakly entangled by all measures, and in fact have the lowest von Neumann entropies among all possible equipartitions of the valence space. In contrast, orbitals with opposite angular momentum projection have relatively large entropies, especially in spherical nuclei. This analysis provides a guide for designing more efficient quantum algorithms for the noisy intermediate-scale quantum era.
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