The ground state energy at unitarity
Abstract
We consider two-component fermions on the lattice in the unitarity limit. This is an idealized limit of attractive fermions where the range of the interaction is zero and the scattering length is infinite. Using Euclidean time projection, we compute the ground state energy using four computationally different but physically identical auxiliary-field methods. The best performance is obtained using a bounded continuous auxiliary field and a non-local updating algorithm called hybrid Monte Carlo. With this method we calculate results for 10 and 14 fermions at lattice volumes 43, 53, 63, 73, 83 and extrapolate to the continuum limit. For 10 fermions in a periodic cube, the ground state energy is 0.292(12) times the ground state energy for non-interacting fermions. For 14 fermions the ratio is 0.329(5).