# Effective theory for ultracold strongly interacting fermionic atoms in two dimensions

## TL;DR

This paper introduces a minimal theoretical model for 2D strongly interacting ultracold Fermi gases, accurately predicting their equation of state and breathing mode frequency, and resolving experimental puzzles related to quantum anomalies.

## Contribution

The authors develop a minimal model requiring two interaction parameters to explain experimental observations in 2D Fermi gases, advancing understanding of quantum anomalies and phase transitions.

## Key findings

- Accurate predictions for equation of state and breathing mode frequency.
- Resolution of experimental puzzles regarding quantum anomaly.
- Identification of conditions to observe quantum anomaly conclusively.

## Abstract

We propose a minimal theoretical model for the description of a two-dimensional (2D) strongly interacting Fermi gas confined transversely in a tight harmonic potential, and present accurate predictions for its equation of state and breathing mode frequency. We show that the minimal model Hamiltonian needs at least two independent interaction parameters, the 2D scattering length and effective range of interactions, in order to quantitatively explain recent experimental measurements at nonzero filling factor $N/N_{2D}$, where $N$ is the total number of atoms and $N_{2D}$ is the threshold number to reach the 2D limit. We therefore resolve in a satisfactory way the puzzling experimental observations of reduced equations of state and reduced quantum anomaly in breathing mode frequency, due to small yet non-negligible $N/N_{2D}$. We argue that a conclusive demonstration of the much-anticipated quantum anomaly is possible at a filling factor of a few percent. Our establishment of the minimal model for 2D ultracold atoms could be crucial to understanding the fermionic Berezinskii-Kosterlitz-Thouless transition in the strongly correlated regime.