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

Understand

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.