Entanglement Rearrangement in Self-Consistent Nuclear Structure Calculations

TL;DR

This paper investigates entanglement properties in nuclear wavefunctions of helium isotopes using various bases, revealing how entanglement measures can inform the efficiency of nuclear structure calculations.

Contribution

It introduces the use of entanglement measures to analyze and compare different basis representations in nuclear many-body calculations, highlighting their potential to improve computational methods.

Findings

Entanglement is more localized in NAT and VNAT bases than in HO basis.

VNAT basis effectively decouples active and inactive spaces.

Entanglement measures can guide basis selection for efficient nuclear calculations.

Abstract

Entanglement properties of $^4$He and $^6$He are investigated using nuclear many-body calculations, specifically the single-nucleon entanglement entropy, and the two-nucleon mutual information and negativity. Nuclear wavefunctions are obtained by performing active-space no-core configuration-interaction calculations using a two-body nucleon-nucleon interaction derived from chiral effective field theory. Entanglement measures within single-particle bases, the harmonic oscillator (HO), Hartree-Fock (HF), natural (NAT) and variational natural (VNAT) bases, are found to exhibit different degrees of complexity. Entanglement in both nuclei is found to be more localized within NAT and VNAT bases than within a HO basis for the optimal HO parameters, and, as anticipated, a core-valence (tensor product) structure emerges from the full six-body calculation of $^{6}$He. The two-nucleon mutual information shows that the VNAT basis, which typically exhibits good convergence properties, effectively decouples the active and inactive spaces. We conclude that measures of one- and two-nucleon entanglement are useful in analyzing the structure of nuclear wave functions, in particular the efficacy of basis states, and may provide useful metrics toward developing more efficient schemes for ab initio computations of the structure and reactions of nuclei, and quantum many-body systems more generally.