Effective theory for ultracold strongly interacting fermionic atoms in two dimensions

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 zero-temperature equation of state and breathing mode frequency based on existing auxiliary-field quantum Monte Carlo data. We show that the minimal model Hamiltonian needs at least two independent interaction parameters, the 2D scattering length and effective range of interactions, to quantitatively explain recent experimental measurements with ultracold 2D fermions. We resolve in a satisfactory way the puzzling experimental observations of the smaller than expected equations of state and breathing mode frequency. Our establishment of the minimal model for 2D fermions is crucial to understand the Berezinskii-Kosterlitz-Thouless transition in the strongly correlated regime.