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Updated: May 21, 2026

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
Published on: August 2, 2019
Quantum anomaly, universal relations, and breathing mode of a two-dimensional Fermi gas
1Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Cambridge CB3 0WA, United Kingdom. j.b.hofmann@damtp.cam.ac.uk
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.
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