Density-functional theory for fermions in the unitary regime

In the unitary regime, fermions interact strongly via two-body potentials that exhibit a zero range and a (negative) infinite scattering length. The energy density is proportional to the energy density of the free Fermi gas with a proportionality constant $\xi$. The author uses a simple density functional parametrized by an effective mass and the universal constant $\xi$, and employs Kohn-Sham density-functional theory to obtain the parameters from fit to one exactly solvable two-body problem. This yields $\xi =0.42$ and a rather large effective mass. The form of the density functional is checked by similar Kohn-Sham calculations for the exactly solvable Calogero model.

Figure 1

(Color online) Density of the harmonically trapped two-fermion system. Exact result (full line) compared to Kohn-Sham results from three different density functionals (dashed lines and dashed-dotted line), and the noninteracting system (dotted line).

Figure 2

(Color online) Densities of the Calogero model for $\beta =4$ for different numbers of particles $N$. Full line: density-functional theory; long-dashed line: long-dashed line: exact density; short-dashed line: Thomas-Fermi theory.