The unitarity limit describes interacting particles where the range of the interaction is zero and the scattering length is infinite. We present precision benchmark calculations for two-component fermions at unitarity using three different ab initio methods: Hamiltonian lattice formalism using iterated eigenvector methods, Euclidean lattice formalism with auxiliary-field projection Monte Carlo, and continuum diffusion Monte Carlo with fixed and released nodes. We have calculated the ground state energy of the unpolarized four-particle system in a periodic cube as a dimensionless fraction of the ground state energy for the non-interacting system. We obtain values 0.211(2) and 0.210(2) using two different Hamiltonian lattice representations, 0.206(9) using Euclidean lattice, and an upper bound of 0.212(2) from fixed-node diffusion Monte Carlo. Released-node calculations starting from the fixed-node result yield a decrease of less than 0.002 over a propagation of 0.4/E_F in Euclidean time, where E_F is the Fermi energy. We find good agreement among all three ab initio methods.Comment: 23 pages, 7 figures, final version to appear in Phys. Rev.
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