Numerical study of the unitary Fermi gas across the superfluid transition

We present results from Monte Carlo calculations investigating the properties of the homogeneous, spin-balanced unitary Fermi gas in three dimensions. The temperature is varied across the superfluid transition allowing us to determine the temperature dependence of the chemical potential, the energy per particle, and the contact density. Numerical artifacts due to finite volume and discretization are systematically studied, estimated, and reduced.

Figure 1

Diamonds correspond to parameters used for individual simulations extrapolated to the thermodynamic limit. The 15 bands indicate the subsets of data included in the continuum ($\nu \to 0$) extrapolations as described in Sec. 3.

Figure 2

Examples of thermodynamic limit extrapolations in the superfluid phase for the filling factor $\nu$ (left panels), the energy per particle $E/N=E/L^3\nu$ (middle panels), and the interaction energy per particle $E_{\mathrm{int}}/N=E_{\mathrm{int}}/L^3\nu$ (right panels), which yields the value of the contact.

Figure 3

Examples of thermodynamic limit extrapolations in the normal phase for the filling factor $\nu$ (left panels), the energy per particle $E/N=E/L^3\nu$ (middle panels), and the interaction energy per particle $E_{\mathrm{int}}/N=E_{\mathrm{int}}/L^3\nu$ (right panels), which yields the value of the contact.

Figure 4

Continuum limit extrapolation along bands of constant $\beta \mu \pm \delta \left(\beta \mu \right)$ (see Fig. 1) for the chemical potential (left panels), the energy density (middle panels), and the contact density (right panels). See further discussion at the end of Sec. 3 regarding the interpolation in $\beta \mu$.

Figure 5

The fit parameter $c_1$ obtained from continuum extrapolations, see Eq. (2), of Monte Carlo data for the chemical potential (top panel), the energy per particle (middle panel), and the contact density (bottom panel).

Figure 6

The chemical potential $\mu /{\varepsilon }_{\mathrm{F}}$ (left panel) and the energy per particle $E/E_{\mathrm{FG}}$ (right panel) in the continuum limit versus $\beta \mu$. We compare our results (red circles; the empty circles denote our results at $T_c$ from Ref. [10]) with experimental data [25] (green squares), as well as with results obtained with bold DMC [14] (blue triangles) and with the Luttinger-Ward formalism [27] (black dashed line). The gray bar indicates the critical point [10] with error margin.

Figure 7

The contact density $\mathcal{C}/{\varepsilon }_{\mathrm{F}}^2=\mathcal{C}/k_{\mathrm{F}}^4$ in the continuum limit versus $\beta \mu$. We compare our results (red circles; the empty circle denotes our result at $T_c$ from Ref. [22]) with experimental data [33] (green squares), as well as results obtained with bold DMC [15] (blue triangles), Luttinger-Ward formalism [34] (black dashed line), and the zero-temperature results from Ref. [35] (cyan line with error margin), Ref. [36] (purple dotted line with error margin), and Ref. [37] (orange dash-dotted line with error margin).