Virial expansion for the Tan contact and Beth-Uhlenbeck formula from 2D SO(2,1) anomalies

Abstract

The relationship between 2D $SO(2,1)$ conformal anomalies in nonrelativistic systems and the virial expansion is explored using recently developed path-integral methods. In the process, the Beth-Uhlenbeck formula for the shift of the second virial coefficient $\delta b_2$ is obtained, as well as a virial expansion for the Tan contact. A possible extension of these techniques for higher orders in the virial expansion is discussed.

9 pages, 2 figures

References in corpus (8)

• Pressure, compressibility, and contact of the two-dimensional attractive Fermi gas
• Path-Integral Fujikawa's Approach to Anomalous Virial Theorems and Equations of State for Systems with $SO(2,1)$ Symmetry
• Path-Integral Derivation of the Non-relativistic Scale Anomaly
• Virial Theorem for Non-relativistic Quantum Fields in D Spatial Dimensions
• Path-Integral Approach to Scale Anomaly at Finite Temperature
• Relationship between Fujikawa's Method and the Background Field Method for the Scale Anomaly
• Bose and Fermi Statistics and the Regularization of the Nonrelativistic Jacobian for the Scale Anomaly
• Dilational Symmetry-Breaking in Thermodynamics

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