BEC-BCS Crossover in Neutron Matter with Renormalization Group based Effective Interactions

TL;DR

This paper investigates the BEC-BCS crossover in neutron matter using renormalization group effective interactions, highlighting the importance of correlations and the reduction of critical temperature near the unitary limit.

Contribution

It introduces a non-mean-field approach to neutron matter in the BEC-BCS crossover using RG-based low-momentum interactions and Weinberg eigenvectors.

Findings

Significant reduction of BCS critical temperature at low densities.

Correlations become increasingly important as neutron matter approaches the unitary limit.

The basis of Weinberg eigenvectors simplifies the use of non-local interactions.

Abstract

We study pure neutron matter in the BEC-BCS crossover regime using renormalization group based low-momentum interactions within the Nozi\`eres-Schmitt-Rink framework. This is an attempt to go beyond the mean field description for low-density matter. We work in the basis of so-called Weinberg eigenvectors where the operator $G_0V$ is diagonal, which proves to be an excellent choice that allows one to use non-local interactions in a very convenient way. We study the importance of correlations as a function of density. We notice that there is a significant reduction of the BCS critical temperature at low-densities as the neutron matter approaches the unitary limit.