Path-Integral Fujikawa's Approach to Anomalous Virial Theorems and Equations of State for Systems with $SO(2,1)$ Symmetry

Abstract

We derive anomalous equations of state for nonrelativistic 2D complex bosonic fields with contact interactions, using Fujikawa's path-integral approach to anomalies and scaling arguments. In the process, we derive an anomalous virial theorem for such systems. The methods used are easily generalizable for other 2D systems, including fermionic ones, and of different spatial dimensionality, all of which share a classical $SO(2,1)$ Schrodinger symmetry. The discussion is of a more formal nature and is intended mainly to shed light on the structure of anomalies in 2D many-body systems. The anomaly corrections to the virial theorem and equation of state - pressure relationship - may be identified as the Tan contact term. The practicality of these ideas rests upon being able to compute in detail the Fujikawa Jacobian that contains the anomaly. This and other conceptual issues, as well as some recent developments, are discussed at the end of the paper.

Final version to be published in Physica A. 13 pages, shorter title, new material added toward the end

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Cited by in corpus (12)

• Virial expansion for the Tan contact and Beth-Uhlenbeck formula from 2D SO(2,1) anomalies
• Virial coefficients of 1D and 2D Fermi gases by stochastic methods and a semiclassical lattice approximation
• Collective modes of ultracold fermionic alkaline-earth gases with SU(N) symmetry
• Fermi-Fermi crossover in the ground state of 1D few-body systems with anomalous three-body interactions
• The virial expansion of attractively interacting Fermi gases in 1D, 2D, and 3D, up to fifth order
• Thermodynamics and static response of anomalous 1D fermions via quantum Monte Carlo in the worldline representation
• Third- and fourth-order virial coefficients of harmonically trapped fermions in a semiclassical approximation
• Spectral density, Levinson's theorem, and the extra term in the second virial coefficient for 1D delta-function potential
• 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
• Quantum anomaly and thermodynamics of one-dimensional fermions with antisymmetric two-body interactions