Unitary Fermi gas, epsilon expansion, and nonrelativistic conformal field theories

TL;DR

This paper reviews theoretical insights into the unitary Fermi gas, focusing on the epsilon expansion technique, conformal invariance, and their implications for thermodynamics, spectra, and experimental realizations.

Contribution

It introduces the epsilon expansion method for UFG and explores the role of conformal symmetry, providing new calculations and connections to nonrelativistic conformal field theories.

Findings

Computed thermodynamic quantities and quasiparticle spectra using epsilon expansion.

Established a correspondence between conformal primary operators and energy eigenstates.

Derived the low-energy effective Lagrangian and shown vanishing bulk viscosities.

Abstract

We review theoretical aspects of unitary Fermi gas (UFG), which has been realized in ultracold atom experiments. We first introduce the epsilon expansion technique based on a systematic expansion in terms of the dimensionality of space. We apply this technique to compute the thermodynamic quantities, the quasiparticle spectrum, and the critical temperature of UFG. We then discuss consequences of the scale and conformal invariance of UFG. We prove a correspondence between primary operators in nonrelativistic conformal field theories and energy eigenstates in a harmonic potential. We use this correspondence to compute energies of fermions at unitarity in a harmonic potential. The scale and conformal invariance together with the general coordinate invariance constrains the properties of UFG. We show the vanishing bulk viscosities of UFG and derive the low-energy effective Lagrangian for the superfluid UFG. Finally we propose other systems exhibiting the nonrelativistic scaling and conformal symmetries that can be in principle realized in ultracold atom experiments.