# Few-body perspective of a quantum anomaly in two-dimensional Fermi gases

## TL;DR

This paper provides precise few-body calculations of the quantum anomaly in two-dimensional Fermi gases, elucidating how effective range influences breathing mode frequencies and aligning well with experimental data.

## Contribution

It offers the first accurate few-body benchmark results on quantum anomaly in 2D Fermi gases, considering effective range effects and extrapolating to many-body systems.

## Key findings

- Quantum anomaly decreases with increasing effective range.
- Maximum anomaly shifts towards weak coupling as effective range grows.
- Extrapolated results agree with experimental observations.

## Abstract

Quantum anomaly manifests itself in the deviation of breathing mode frequency from the scale invariant value of $2\omega$ in two-dimensional harmonically trapped Fermi gases, where $\omega$ is the trapping frequency. Its recent experimental observation with cold-atoms reveals an unexpected role played by the effective range of interactions, which requires quantitative theoretical understanding. Here we provide accurate, benchmark results on quantum anomaly from a few-body perspective. We consider the breathing mode of a few trapped interacting fermions in two dimensions up to six particles and present the mode frequency as a function of scattering length for a wide range of effective range. We show that the maximum quantum anomaly gradually reduces as effective range increases while the maximum position shifts towards the weak-coupling limit. We extrapolate our few-body results to the many-body limit and find a good agreement with the experimental measurements. Our results may also be directly applicable to a few-fermion system prepared in microtraps and optical tweezers.