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

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

2011-12-06

arxiv.org/abs/1112.1384v2

Physics

Condensed Matter

Quantum Gases

5 pages, 1 figure; v2: revised version, accepted for publication in PRL

Scientific paper

In this paper, we show that the hidden SL(2,R) 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 which 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.

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