Mode entanglement and isospin pairing in two-nucleon systems

TL;DR

This paper investigates how entanglement and correlations in two-nucleon systems are influenced by isospin formalism and pairing interactions, revealing the impact of shell structure and angular momentum coupling on entanglement measures.

Contribution

It provides analytical expressions for entanglement measures in two-nucleon systems and analyzes the effects of pairing interactions and shell structure on entanglement.

Findings

Pairing interactions can maximize one-body entanglement entropy in ground states.

Shell structure and angular momentum coupling significantly influence entanglement.

Conservation of angular momentum and isospin affects one-mode entropies regardless of particle number.

Abstract

In this study, we explore the entanglement and correlation in two-nucleon systems using isospin formalism. With the help of Slater decomposition, we derive analytical expressions for various entanglement measures. Specifically, we analyse the one- and two-mode entropies, mutual informations, and a basis-independent characteristic known as the one-body entanglement entropy. To understand the impact of pairing, we consider interactions involving isovector and isoscalar L=0 pairing terms. Our findings show that certain pairing interactions can maximize one-body entanglement entropy of ground states when both total angular momentum and total isospin have zero projections. We provide numerical examples for the sd shell and explore the mutual informations in LS coupled and jj coupled single-particle bases. We find that the shell structure and angular momentum coupling significantly impact the measures of entanglement. We outline the implications of conserving angular momentum and isospin on one-mode entropies, irrespective of particle number.