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Canadian Journal of Physics

Quantum phase transition in even–even molybdenum isotopes using von Neumann entropy

Narjes Amiri, M Sayedi, Maryam Ghapanvari, M. A. Jafarizadeh

Published Dec 3, 2024• 0 citations
Publisher

Abstract

In this study, the von Neumann entropy (entanglement entropy) of s– d bosons and proton (π)–neutron (ν) bosons in the even–even molybdenum (94–102Mo) isotopes, within the framework of the Interacting Boson Model-2, has been calculated and analyzed. In order to compare the results, the energy spectra, quadrupole moment, and the expectation value of the s-boson number operator of Mo isotopes have been obtained. The results showed that 94Mo has the minimum entanglement of s and d bosons and 102Mo nucleus has the maximum entanglement of s and d bosons. Therefore, these nuclei are spherical (U(5)) and γ-unstable (SO(6)) nuclei, respectively, and other observables confirm this result. Also, the value of the entanglement entropy of the π and ν bosons is constant by changing the control parameter. So, it does not show any transition.

DOI
10.1139/cjp-2024-0113

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In this study, the von Neumann entropy (entanglement entropy) of s– d bosons and proton (π)–neutron (ν) bosons in the even–even molybdenum (94–102Mo) isotopes, within the framework of the Interacting Boson Model-2, has been calculated and analyzed. In order to compare the results, the energy spectra, quadrupole moment, and the expectation value of the s-boson number operator of Mo isotopes have been obtained. The results showed that 94Mo has the minimum entanglement of s and d bosons and 102Mo nucleus has the maximum entanglement of s and d bosons. Therefore, these nuclei are spherical (U(5)) and γ-unstable (SO(6)) nuclei, respectively, and other observables confirm this result. Also, the value of the entanglement entropy of the π and ν bosons is constant by changing the control parameter. So, it does not show any transition.
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Abstract In this work, the von Neumann entropy has been calculated and employed as a probe to analyse quantum phase transitions (QPTs) within the -Interacting Boson Model ( -IBM). The von Neumann entropy between the -boson and -boson sectors is used as an indicator of QPTs and as a robust observable for the theoretical analysis of the isotopes. The von Neumann entropy correctly characterises the QPT in the transition region. The numerical results show that the and isotopes are located in the and limits, respectively.
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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The entanglement of the N-harmonium system (i.e., a completely-integrable model of N particles where both the confinement and the two-particle interaction are har-monic) is shown to be analytically determined in terms of N and the relative interaction strength. First, the entanglement of the N-boson system via the von Neumann entropy is computed by use of the corresponding natural occupation numbers. Below a critical value Nc of N it is found that, for positive values of the coupling constant the entan-glement grows when the number of particles is increasing; opposite situation occurs for N> Nc. Then the entanglement of the N-fermion system is investigated by means of the linear entropy, which is a linearized form of the von Neumann entropy of the one-body reduced density matrix. We have shown that the entanglement grows when the number of particles is increasing in the region of negative coupling. For positively increasing values of the coupling the entanglement as a function of N varies according to various regimes. Moreover, in the strong coupling regime the entropy of the system decreases when N is growing. For fixed N, the entanglement is found (a) to decrease (increase) for negatively (positively) increasing values of the coupling constant, and (b) to grow when the energy is increasing. Finally, let us point out that the spatial and spin contributions to the total entanglement are of comparable size.
Analysis of the U(5)↔SU(3)U(5)\leftrightarrow SU(3)U(5)↔SU(3) transitional region from an entanglement-based perspective
The degree of entanglement between components of a bipartite system can serve as a useful criterion for studying Quantum Phase Transitions (QPT). The von Neumann entropy and generalized concurrence serve as measures, while Schmidt number and Schmidt gap are quantifiers; together, they are key tools for identifying QPT. Using these tools, we have examined the QPT in the [Formula: see text] region within the first version of the semiclassical approximation of the Interacting Boson Model (IBM-1). Additionally, the Kullback-Leibler divergence (KLD) was employed as a criterion to compare two probability distribution functions in order to identify the transition region and the critical point. The theoretical results indicated that the Schmidt number and Schmidt gap, the von Neumann entropy, generalized concurrence, and the KLD can characterize the transition behavior and critical point (X(5)) in this region. To verify these results in real nuclei, the Dysprosium isotopic chain was selected. Using the suggested entanglement measures, the symmetry limits and the critical point were identified. The results obtained are fully consistent with experimental evidence.