Numerical Portrait of a Relativistic BCS Gapped Superfluid

TL;DR

This paper numerically investigates a 3+1D NJL model at high density, demonstrating the emergence of a BCS superfluid phase with a measurable energy gap, and explores its stability and effects of isospin asymmetry.

Contribution

It provides the first numerical evidence of a BCS superfluid phase in a 3+1D NJL model at high density, including measurements of the energy gap and stability analysis.

Findings

Ground state at high chemical potential is a BCS superfluid.

Energy gap is approximately 15% of the vacuum fermion mass at mu a=0.8.

The BCS phase remains stable against thermal fluctuations.

Abstract

We present results of numerical simulations of the 3+1 dimensional Nambu - Jona-Lasinio (NJL) model with a non-zero baryon density enforced via the introduction of a chemical potential mu not equal to 0. The triviality of the model with a number of dimensions d>=4 is dealt with by fitting low energy constants, calculated analytically in the large number of colors (Hartree) limit, to phenomenological values. Non-perturbative measurements of local order parameters for superfluidity and their related susceptibilities show that, in contrast to the 2+1 dimensional model, the ground-state at high chemical potential and low temperature is that of a traditional BCS superfluid. This conclusion is supported by the direct observation of a gap in the dispersion relation for 0.5<=(mu a)<=0.85, which at (mu a)=0.8 is found to be roughly 15% the size of the vacuum fermion mass. We also present results of an initial investigation of the stability of the BCS phase against thermal fluctuations. Finally, we discuss the effect of splitting the Fermi surfaces of the pairing partners by the introduction of a non-zero isospin chemical potential.