Pairing correlations and eigenvalues of two-body density matrix in atomic nuclei

TL;DR

This paper investigates how the largest eigenvalue of the two-body density matrix signals superfluid or paired phases in atomic nuclei, revealing clear phase transitions for like-particle pairing but not for proton-neutron pairing.

Contribution

It applies the Yang Off-Diagonal Long Range Order criterion to various nuclear Hamiltonians, highlighting differences in phase transition signatures.

Findings

Largest eigenvalue indicates phase transition in like-particle pairing

No clear eigenvalue change for proton-neutron pairing in self-conjugate nuclei

Differentiates pairing types based on eigenvalue behavior

Abstract

The quantum phases of superconductivity and superfluidity are characterised mathematically by the Yang concept of Off-Diagonal Long Range Order (ODLRO), related to the existence of a large eigenvalue of the density matrix. We analyse how the Yang criterion applies for various Hamiltonians commonly employed to describe superfluid-type correlations in atomic nuclei. For like-particle pairing Hamiltonians the behaviour of the largest eigenvalue of two-body density matrix shows a clear evidence for a transition between a normal to a paired phase. However, this is not the case for the isoscalar proton-neutron pairing interactions acting in self-conjugate nuclei.