A BCS Gapped Superfluid on the Lattice

TL;DR

This paper presents numerical evidence that the 3+1D NJL model at high density exhibits a BCS superfluid phase with a diquark gap roughly 15% of the fermion mass, indicating a superfluid transition driven by diquark condensation.

Contribution

It demonstrates the existence of a BCS superfluid phase in the NJL model at high density and characterizes the diquark gap and symmetry breaking in this phase.

Findings

Diquark condensate proportional to Fermi surface area

Energy gap approximately 15% of vacuum fermion mass

Transition from broken to restored chiral symmetry at high density

Abstract

We discuss results of numerical analyses of the 3+1 dimensional Nambu--Jona-Lasinio model at non-zero baryon density. By studying relevant order parameters, it is shown that the model goes through a transition between a vacuum with broken chiral symmetry, and a chirally restored phase at high baryon chemical potential (mu) with a diquark condensate roughly proportional to the area of the Fermi surface and a broken U(1) baryon number symmetry. The condensation of diquark pairs from the fermionic spectrum is shown to lead to an energy gap (Delta) about the Fermi energy (E_F), which is found to be approximately 15% of the vacuum fermion mass and roughly independent of mu in the chirally restored phase. The ground-state is believed, therefore, to be that of a BCS superfluid. We also discuss the effect of simulating on a finite volume, and any caveats this places on the conclusions made above.