Finite-Temperature Pairing Gap of a Unitary Fermi Gas by Quantum Monte Carlo Calculations

We calculate the one-body temperature Green’s (Matsubara) function of the unitary Fermi gas via quantum Monte Carlo, and extract the spectral weight function $A(p,\omega )$ using the methods of maximum entropy and singular value decomposition. From $A(p,\omega )$ we determine the quasiparticle spectrum, which can be accurately parametrized by three functions of temperature: an effective mass $m^{*}$, a mean-field potential $U$, and a gap $\Delta$. Below the critical temperature $T_c=0.15{\epsilon }_F$ the results for $m^{*}$, $U$, and $\Delta$ can be accurately reproduced using an independent quasiparticle model. We find evidence of a pseudogap in the fermionic excitation spectrum for temperatures up to $T^{*}\approx 0.20{\epsilon }_F>T_c$.

Figure 1

Spectral weight function $A(\mathit{p},\omega )$ for three temperatures: $T=0.15{\epsilon }_F\approx T_c$ (left upper panel), $T=0.18{\epsilon }_F$ (right upper panel), and $T=0.20{\epsilon }_F$ (lower panel). The presence of a gap in clearly seen in the upper two panels.

Figure 2

Quasiparticle energies $E(\mathit{p})$ (squares) extracted from the spectral weight function $A(\mathit{p},\omega )$ at $T=0.1{\epsilon }_F$. The line corresponds to the fit to Eq. (8). The circles are the results of Carlson and Reddy [4].

Figure 3

The single-particle parameters extracted from the spectral weight function at unitarity. The dashed, solid, and dotted lines represent the quantities: $m/m^{*}$, $\Delta /{\epsilon }_F$, $U/{\epsilon }_F$, respectively, extracted using the assumption of independent quasiparticle model.