Dynamical violation of scale invariance and the dilaton in a cold Fermi gas

TL;DR

This paper predicts a new phase in a two-dimensional cold Fermi gas where approximate scale symmetry is broken, leading to a dilaton mode and an anomalously large compressibility, with a quantum phase transition driven by chemical potential.

Contribution

It introduces a novel scale symmetry breaking phase in a 2D Fermi gas and identifies the dilaton as a collective excitation within this phase.

Findings

Existence of a stable scale symmetry breaking phase.

Identification of the dilaton as a collective mode.

Anomalously large compressibility at the critical density.

Abstract

We use the large N approximation to find an exotic phase of a cold, two-dimensional, N-component Fermi gas which exhibits dynamically broken approximate scale symmetry. We identify a particular weakly damped collective excitation as the dilaton, the pseudo-Goldstone boson associated with the broken approximate scale symmetry. We argue that the symmetry breaking phase is stable for a range of parameters of the theory and there is a fluctuation induced first order quantum phase transition between the normal and the scale symmetry breaking phases which can be driven by tuning the chemical potential. We find that the compressibility of the gas at its lower critical density is anomalously large, 2N times that of a perfect gas at the same density.