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

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 Tc 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 ≤ (kF a) −1 ≤ 0.2, where a is the s-wave scattering length and kF 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 T0 > Tc, which depends on the coupling and is obtained by studying the deviation of the caloric curve from that of a free Fermi gas. For Tc < 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.

Thermodynamics of Ultracold Fermi Gases

“…It is compared in Table 4.1 to several theoretical results. Our measurement is in very good agreement with the most robust numerical calculations [113,172,173]. It is also interesting to extract from our data the value of T /T F at the phase transition, where k B T F = 2 /2m(3π 2 n) 2/3 is the Fermi energy.…”

“…also in good agreement with [113,172,173]. In addition, we deduce from this calculation the chemical potential value at the phase transition:…”

“…This intuitively explains why collective modes do not easily discriminate between theories. [141] (gray squares), a quantum Monte-Carlo calculation from [173] (gray open circles) and a diagrammatic approach from [138] (gray crosses). The dashed line is calculated from a t of the Fixed-Node data [67].…”

“…• a quantum Monte-Carlo calculation from [173], extrapolated at T = 0, • a diagrammatic approach from [138].…”

Lattice Monte Carlo calculations for unitary fermions in a harmonic trap

“…We choose to realize the lattice Laplacian in such a way that D has the following form in momentum space ( [27]):…”