Density functional theory for non-relativistic fermions in the unitarity limit

We derive an energy density functional for non-relativistic spin one-half fermions in the limit of a divergent two-body scattering length. Using an epsilon expansion around d=4−ε spatial dimensions we compute the coefficient of the leading correction beyond the local density approximation (LDA). In the case of N fermionic atoms trapped in a harmonic potential this correction has the form E=ELDA(1+cs(3N)−2/3), where ELDA is the total energy in LDA approximation. At next-to-leading order in the epsilon expansion we find cs=1.68, which is significantly larger than the result for non-interacting fermions, cs=0.5.