Quantum Monte Carlo Simulations of the BCS-BEC Crossover at Finite Temperature

TL;DR

This paper develops a Quantum Monte Carlo method to study the finite-temperature behavior of spin 1/2 fermions across the BCS-BEC crossover, providing insights into superfluid transition temperatures and pairing effects.

Contribution

It introduces a formalism and algorithm for finite-temperature QMC simulations of dilute fermionic systems with s-wave interactions, focusing on the BCS-BEC crossover regime.

Findings

Upper bounds on critical temperature T_c for superfluidity.

Deviations from normal Fermi gas behavior above T_c due to pairing.

Comparison of low-temperature energy and pairing gap with other Monte Carlo results.

Abstract

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 \le (k_F a)^{-1} \le 0.2, where a is the s-wave scattering length and k_F is the Fermi momentum of a non-interacting gas at the same density. In all cases our data is consistent with normal Fermi gas behavior above a characteristic temperature T_0 > 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 < T_0 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.