Effective-range dependence of two-dimensional Fermi gases

The Feshbach resonance provides precise control over the scattering length and effective range of interactions between ultracold atoms. We propose the ultratransferable pseudopotential to model effective interaction ranges $-1.5 \leq k_\mathrm{F}^2 R_\mathrm{eff}^2 \leq 0$, here $R_\mathrm{eff}$ is the effective range and $k_\mathrm{F}$ is the Fermi wave vector, describing narrow to broad Feshbach resonances. We develop a mean-field treatment and exploit the pseudopotential to perform a variational and diffusion Monte Carlo study of the ground state of the two-dimensional Fermi gas, reporting on the ground-state energy, contact, condensate fraction, momentum distribution, and pair-correlation functions as a function of the effective interaction range across the BEC-BCS crossover. The limit $k_\mathrm{F}^2 R_\mathrm{eff}^2 \to -\infty$ is a gas of bosons with zero binding energy, whereas $\ln(k_\mathrm{F} a) \to -\infty$ corresponds to noninteracting bosons with infinite binding energy.