Constrained Path Monte Carlo method for spin $ 1/2 $ fermions at unitarity limit

We present calculations for spin $1/2$ fermions at unitarity limit, where the effective range of the interaction is zero and the scattering length is infinite. We compute the ground-state energy for a system of 6, 10,14,18 and 20 particles, with equal numbers of up and down spins in a periodic cube in the full ground-state constrained-path Monte Carlo (CPMC) method using the extended, attractive Hubbard model. Our results in a careful extrapolation to the thermodynamic limit may suggest that the ratio of the ground-state energy to that of a free Fermi gas is $\xi = 0.43(4)$, which can compare with recent experimental results and consistent with the fixed node Green's function Monte Carlo and novel lattice approaches results. We also obtain results for interactions with different effective ranges and find that the energy is consistent with a universal linear dependence on the product of the Fermi momentum and the effective range.