Precision benchmark calculations for four particles at unitarity

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 methods, and continuum diffusion Monte Carlo methods 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 noninteracting system. We obtain values of 0.211(2) and 0.210(2) using two different Hamiltonian lattice representations, 0.206(9) using Euclidean lattice formalism, and an upper bound of 0.212(2) from fixed-node diffusion Monte Carlo methods. Released-node calculations starting from the fixed-node result yield a decrease of less than 0.002 over a propagation of 0.4E(F)(-1) in Euclidean time, where E-F is the Fermi energy. We find good agreement among all three ab initio methods.