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arXiv:2210.14338 · Journal of Physics G Nuclear and Particle Physics

Proton-neutron entanglement in the nuclear shell model

Calvin W. Johnson, Oliver C. Gorton

Published Feb 24, 2023• 48 citations
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Abstract

Abstract We compute the proton-neutron entanglement entropy in the interacting nuclear shell model for a variety of nuclides and interactions. Some results make intuitive sense, for example, that the shell structure, as governed by single-particle and monopole energies, strongly affects the energetically available space and thus the entanglement entropy. We also find a surprising result: that the entanglement entropy at low excitation energy tends to decrease for nuclides when N ≠ Z. While we provide evidence this arises from the physical nuclear force by contrasting with random two-body interactions which shows no such decrease, the exact mechanism is unclear. Nonetheless, the low entanglement suggests that in models of neutron-rich nuclides, the coupling between protons and neutrons may be less computationally demanding than one might otherwise expect.

DOI
10.1088/1361-6471/acbece

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The interacting shell model, a configuration-interaction method, is a venerable approach for low-lying nuclear structure calculations, but it is hampered by the exponential growth of its basis dimension as one increases the single-particle space and/or the number of active particles. Recent, quantum-information-inspired work has demonstrated that the proton and neutron sectors of a nuclear wave function are weakly entangled. Furthermore, the entanglement is smaller for nuclides away from N=ZN=ZN=Z, such as heavy, neutron-rich nuclides. Here we implement a weak entanglement approximation to bipartite configuration-interaction wave functions, approximating low-lying levels by coupling a relatively small number of many-proton and many-neutron states. This truncation scheme, which we present in the context of past approaches, reduces the basis dimension by many orders of magnitude while preserving essential features of nuclear spectra.
We report on a recently proposed approach, inspired by quantum information theory, for calculating low-energy nuclear structure in the framework of the configuration-interaction shell-model. Empirical evidence has demonstrated that the many-proton and many-neutron partitions of nuclear configuration-interaction wave functions are weakly entangled, especially away from N = Z . This has been developed into a practical methodology, the Proton And Neutron Approximate Shell-model (PANASh). We review the basic ideas and present recent results. We also discuss some technical developments in calculations.
We report on a recently proposed approach, inspired by quantum informationtheory, for calculating low-energy nuclear structure in the framework of the configuration-interaction shell-model. Empirical evidence has demonstrated that the many-proton and many-neutron partitions of nuclear configuration-interaction wave functions are weakly entangled, especially away from N=ZN=ZN=Z. This has been developed into a practical methodology, the Proton And Neutron Approximate Shell-model (PANASh). We review the basic ideas and present recent results. We also discuss some technical developments in calculations.
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.
The nuclear shell model is a useful and widely used tool for nuclear structure, but it can be hampered by the exponential growth of the basis. Drawing inspiration from quantum information theory, one can show that the proton and neutron components are typically weakly entangled. This has led to the Proton And Neutron Approximate Shell-model (PANASh). I review the underlying ideas and present recent developments. In particular I show how PANASh can accelerate beyond-mean-field methods such as the generator coordinate method.
Abstract We investigate the spin entanglement in few-nucleon scattering processes involving nucleons and deuterons. For this purpose, we consider the entanglement power introduced by Beane et al. We analyze different entanglement entropies as a basis to define the entanglement power of the strong interaction and calculate the corresponding entanglement powers for proton–neutron, neutron–deuteron, proton–deuteron, and deuteron–deuteron scattering. For the latter two processes, we also take into account the modification from the Coulomb interaction. In contrast to proton–neutron scattering, no universal low-energy features are evident in the spin entanglement in neutron–deuteron, proton–deuteron, and deuteron–deuteron scattering.