Symmetry Obstruction to Fermi Liquid Behavior in the Unitary Limit

TL;DR

This paper demonstrates that in the unitary limit, a three-dimensional Fermi gas cannot be described by Fermi Liquid Theory due to symmetry obstructions related to boost and conformal invariance.

Contribution

It reveals fundamental symmetry constraints preventing Fermi Liquid behavior in the unitary Fermi gas at certain temperature regimes.

Findings

Fermi gas in the unitary limit cannot be described by FLT

No effective field theory captures both Fermi liquid behavior and broken boost/conformal invariance

Symmetry considerations obstruct Fermi liquid description in this regime

Abstract

We show that a Fermi gas, in three dimensions, at temperatures above the superconducting phase transition but below the Fermi temperature, can not be described by Fermi Liquid Theory (FLT) in the unitary limit where the scattering length diverges. The result follows by showing that the there are no effective field theory descriptions that both behave like a Fermi liquid and properly non-linearly realize the spontaneously broken boost and conformal invariance of the system.