Gapless Superfluid in $SU(2n+1)$ Fermions Systems

TL;DR

This paper proves that in a generalized Hubbard model with an odd number of fermion species, the ground state is a gapless superfluid with a full Fermi surface coexisting with superfluidity, using Grassmannian integration techniques.

Contribution

It establishes the existence of a gapless superfluid phase in $SU(2n+1)$ fermion systems at the mean field level, regardless of interaction strength.

Findings

Existence of a gapless superfluid in odd-species fermion systems.

Coexistence of a full Fermi surface with superfluidity.

Presence of a free mode in strongly interacting regimes.

Abstract

We investigate the generalized Hubbard model of $(2n+1)$ Fermion species interacting via a symmetric contact attraction potential. We prove that the ground state of such system is a gapless superfluid, where a full Fermi surface coexists with a superfluid. Moreover, doing so we prove the existence of a free mode in a strongly interacting system, regardless of the potential strength. This proof holds at the mean field level. A Grassmannian Gaussian integration technique is used to deal with the problem. Our predictions may be relevant to future high-spin cold atoms experiments.