Quantum anomaly, universal relations, and breathing mode of a two-dimensional Fermi gas

TL;DR

This paper investigates how quantum effects break classical symmetry in a two-dimensional Fermi gas, leading to anomalous corrections that influence the system's virial theorem, pressure relations, and breathing mode frequency shifts, with experimental comparisons.

Contribution

It introduces the quantum anomaly's impact on symmetry and derives universal relations and frequency shifts for the 2D Fermi gas, connecting theory with recent experiments.

Findings

Quantum anomaly breaks classical SO(2,1) symmetry.

Derived universal pressure relation for homogeneous gas.

Estimated frequency shift of breathing mode at zero temperature.

Abstract

In this Letter, we show that the classical SO(2,1) symmetry of a harmonically trapped Fermi gas in two dimensions is broken by quantum effects. The anomalous correction to the symmetry algebra is given by a two-body operator that is well known as the contact. Taking into account this modification, we are able to derive the virial theorem for the system and a universal relation for the pressure of a homogeneous gas. The existence of an undamped breathing mode is associated with the classical symmetry. We provide an estimate for the anomalous frequency shift of this oscillation at zero temperature and compare the result with a recent experiment by [E. Vogt et al., Phys. Rev. Lett. 108, 070404 (2012)]. Discrepancies are attributed to finite temperature effects.