  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.
