Apparent low-energy scale invariance in two-dimensional Fermi gases

TL;DR

This paper derives exact relations for two-dimensional Fermi gases to explain the observed near scale-invariance of breathing modes across the BCS-BEC crossover, highlighting the special role of 2D interactions.

Contribution

It provides exact theoretical results linking mode frequency shifts to thermodynamic quantities and dissipation, clarifying the apparent scale invariance in 2D Fermi gases.

Findings

The mode frequency shift relates to a thermodynamic quantity $\gamma_d$.

$\gamma_2$ is small in both BCS and BEC regimes due to logarithmic interaction dependence.

The analysis explains the near scale-invariance despite the presence of a scale in the system.

Abstract

Recent experiments on a $\2d$ Fermi gas find an undamped breathing mode at twice the trap frequency over a wide range of parameters. To understand this seemingly scale-invariant behavior in a system with a scale, we derive two exact results valid across the entire BCS-BEC crossover at all temperatures. First, we relate the shift of the mode frequency from its scale-invariant value to $\gamma_d \equiv (1+2/d)P-\rho(\partial P/\partial\rho)_s$ in $d$ dimensions. Next, we relate $\gamma_d$ to dissipation via a new low-energy bulk viscosity sum rule. We argue that $\2d$ is special, with its logarithmic dependence of the interaction on density, and thus $\gamma_2$ is small in both the BCS and BEC regimes, even though $P - 2\varepsilon/d$, sensitive to the dimer binding energy that breaks scale invariance, is not.