Critical Temperature and Thermodynamics of Attractive Fermions at Unitarity

The unitarity regime of the BCS-BEC crossover can be realized by diluting a system of two-component lattice fermions with an on-site attractive interaction. We perform a systematic-error-free finite-temperature simulation of this system by diagrammatic determinant Monte Carlo method. The critical temperature in units of Fermi energy is found to be $T_c/{\epsilon }_F=0.152(7)$. We also report the behavior of the thermodynamic functions, and discuss the issues of thermometry of ultracold Fermi gases.

Figure 1

A sketch of a vertex configuration for the correlation function. Brown dots are the four-point vertices, with the incoming and outgoing lines shown. Red diamonds represent the two-point vertices corresponding to $P(\mathbf{x},\tau )$ and $P^{†}({\mathbf{x}}^{\prime },{\tau }^{\prime })$. See the text for discussion.

Figure 2

A typical crossing of the $R(L,T)$ curves. The error bars are $2\sigma$, and solid lines are the linear fits to the MC points. The data are for the $\mu =-5.2t$, thus $\nu (T=T_c,L\to \infty )=0.148(1)$.

Figure 3

The scaling of the lattice critical temperature with filling factor (circles). The error bars are 1 standard deviation. The results of Refs. 23, 24 at quarter filling are also shown for a comparison. See the text for discussion.

Figure 4

The temperature dependence of the energy per particle (upper panel) and chemical potential (lower panel) of the unitary Fermi gas. Red circles are the MC results, black dotted lines and blue dashed lines correspond to the Boltzmann and noninteracting Fermi gases, respectively, the dot-dashed lines are the asymptotic predictions of Ref. 29 (plus the first virial Fermi correction), black triangles are the path integral MC results of Ref. 16, and the purple stars denote the ground-state fixed-node MC results [15].