Large-N expansion for unitary superfluid Fermi gases

TL;DR

This paper develops a large-N expansion method to analyze strongly interacting unitary Fermi gases, providing systematic corrections to mean-field theory and predicting key thermodynamic quantities for the physical case.

Contribution

It introduces a large-N expansion framework for unitary Fermi gases, enabling systematic calculation of thermodynamic properties beyond mean-field approximation.

Findings

Predicted energy ratio .28 times non-interacting gas

Predicted pairing gap .52 times Fermi energy

Provided corrections to mean-field results near unitarity

Abstract

We analyze strongly interacting Fermi gases in the unitary regime by considering the generalization to an arbitrary number N of spin-1/2 fermion flavors with Sp(2N) symmetry. For N=\infty this problem is exactly solved by the BCS-BEC mean-field theory, with corrections small in the parameter 1/N. The large-N expansion provides a systematic way to determine corrections to mean-field predictions, allowing the calculation of a variety of thermodynamic quantities at (and in the proximity to) unitarity, including the energy, the pairing gap, and upper-critical polarization (in the case of a polarized gas) for the normal to superfluid instability. For the physical case of N=1, among other quantities, we predict in the unitarity regime, the energy of the gas to be \xi=0.28 times that for the non-interacting gas and the pairing gap to be 0.52 times the Fermi energy.