Effective Lagrangian of unitary Fermi gas from $\varepsilon$ expansion

TL;DR

This paper derives an effective Ginzburg-Landau-like functional for the unitary Fermi gas using the epsilon expansion, enabling analysis of vortex structures and phase interfaces with improved accuracy.

Contribution

It extends the epsilon expansion method to next-to-leading order, providing a more precise effective Lagrangian for the unitary Fermi gas.

Findings

Surface free energy is approximately four times larger than previous estimates.

Leading order terms suffice for many practical scenarios.

Functional successfully describes vortex and phase interface structures.

Abstract

Using $\varepsilon$ expansion technique proposed in \cite{Nishida:2006br} we derive an effective Lagrangian (Ginzburg-Landau-like functional) of the degenerate unitary Fermi gas to the next-to-leading (NLO) order in $\varepsilon.$ It is demonstrated that for many realistic situations it is sufficient to retain leading order (LO) terms in the derivative expansion. The functional is used to study vortex structure in the symmetric gas, and interface between normal and superfluid phases in the polarized gas. The resulting surface free energy is about four times larger than the value previously quoted in the literature.