Local-density-functional theory for superfluid fermionic systems: The unitary gas

The first detailed comparison between ab initio calculations of finite fermionic superfluid systems, performed recently by Chang and Bertsch [Phys. Rev. A 76, 021603(R) (2007)] and by von Stecher, Grange, and Blume [e-print arXiv:0705.0671v1] and the extension of the density-functional theory superfluid local-density approximation (SLDA) is presented. It is shown that SLDA reproduces the total energies, number density distributions in inhomogeneous systems along with the energy of the normal state in homogeneous systems. Unlike the Kohn-Sham LDA, in SLDA the effective fermion mass differs from the bare fermion mass and the spectrum of elementary excitations is also reproduced.

Figure 1

(Color online) The ab initio fermionic quasiparticle spectrum determined in Ref. 11 (red circles) compared with the SLDA spectrum defined by the ab initio parameters $\xi ,\eta$ from Ref. 11 (solid blue line), [10] (dotted blue line), [12] (dashed blue line), and naive BCS approximation at unitarity (black dotted-dashed line).

Figure 2

(Color online) The comparison between the GFMC [14], FN-DMC [15], and SLDA total energies $E\left(N\right)$. The clear odd-even staggering of the energies is due to the onset of the pairing correlations. The inset shows the discrepancy between the GFMC and FN-DMC and SLDA energies, $\delta E\left(N\right)=E_{\mathit{MC}}\left(N\right)∕E_{\mathit{SLDA}}\left(N\right)-1$, where $E_{\mathit{MC}}\left(N\right)$ stands for the energies obtained in GFMC or FN-DMC, respectively.

Figure 3

(Color online) The pairing field $\Delta \left(\mathbf{r}\right)$ for even particle number systems. The inset shows the quantity ${\delta }_{2}E\left(N\right)=E\left(N\right)-[E(N+1)+E(N-1)]∕2$ calculated in SLDA (red squares) and GFMC (blue circles).