Quantum Monte Carlo simulations of the BCS-BEC crossover at finite temperature

The quantum Monte Carlo method for spin-1/2 fermions at finite temperature is formulated for dilute systems with an s-wave interaction. The motivation and the formalism are discussed along with descriptions of the algorithm and various numerical issues. We report on results for the energy, entropy, and chemical potential as a function of temperature. We give upper bounds on the critical temperature T_c for the onset of superfluidity, obtained by studying the finite-size scaling of the condensate fraction. All of these quantities were computed for couplings around the unitary regime in the range −0.5⩽(k_Fa)⁻¹⩽0.2, where a is the s-wave scattering length and k_F is the Fermi momentum of a noninteracting gas at the same density. In all cases our data are consistent with normal Fermi gas behavior above a characteristic temperature T₀>T_c, which depends on the coupling and is obtained by studying the deviation of the caloric curve from that of a free Fermi gas. For T_c<T<T₀ we find deviations from normal Fermi gas behavior that can be attributed to pairing effects. Low-temperature results for the energy and the pairing gap are shown and compared with Green-function Monte Carlo results by other groups.