Nonrelativistic Conformal Invariance in Mesoscopic Two-Dimensional Fermi Gases

TL;DR

This paper demonstrates that nonrelativistic conformal symmetry persists in weakly interacting mesoscopic two-dimensional Fermi gases, verified through energy spectrum analysis and distribution functions, with implications for current experiments.

Contribution

It shows the existence of a conformal window at weak interactions in 2D Fermi gases and verifies conformal symmetry using perturbation theory and numerical sampling.

Findings

Energy spectrum exhibits conformal towers with specific excitation energies.

Analytical form of the hyperradial distribution function matches predictions.

Conformal symmetry is observable in current mesoscopic Fermi gas experiments.

Abstract

Two-dimensional Fermi gases with universal short-range interactions are known to exhibit a quantum anomaly, where a classical scale and conformal invariance is broken by quantum effects at strong coupling. We argue that in a quasi two-dimensional geometry, a conformal window remains at weak interactions. Using degenerate perturbation theory, we verify the conformal symmetry by computing the energy spectrum of mesoscopic particle ensembles in a harmonic trap, which separates into conformal towers formed by so-called primary states and their center-of-mass and breathing-mode excitations, the latter having excitation energies at precisely twice the harmonic oscillator energy. In addition, using Metropolis importance sampling, we compute the hyperradial distribution function of the many-body wave functions, which are predicted by the conformal symmetry in closed analytical form. The weakly interacting Fermi gas constitutes a system where the nonrelativistic conformal symmetry can be revealed using elementary methods, and our results are testable in current experiments on mesoscopic Fermi gases.