Entanglement and correlation in two-nucleon systems

TL;DR

This paper investigates entanglement and correlation in two-nucleon systems, deriving analytical measures and analyzing their behavior in shell model configurations, highlighting maximally entangled states at zero angular momentum.

Contribution

It introduces analytical expressions for entanglement measures in two-nucleon systems using the Slater decomposition and explores their properties in shell model states.

Findings

Maximal entanglement occurs at zero total angular momentum.

One- and two-mode entropies are equal for finite modes.

Ground state entanglement entropy is near maximal.

Abstract

We examine the mode entanglement and correlation of two fermionic particles. We study the one- and two-mode entropy and a global characteristic, the one-body entanglement entropy. We consider not only angular momentum coupled states with single configuration but use the configuration interaction method. With the help of the Slater decomposition, we derive analytical expressions for the entanglement measures. We show that when the total angular momentum is zero specific single configurations describe maximally entangled states. It turns out that for a finite number of associated modes the one- and two-mode entropies have identical values. In the shell model framework, we numerically study two valence neutrons in the $sd$ shell. The one-body entanglement entropy of the ground state is close to the maximal value and the associated modes have the largest mutual information.