Incorporating exact two-body propagators for zero-range interactions into $N$-body Monte Carlo simulations

Ultracold atomic gases are, to a very good approximation, described by pairwise zero-range interactions. This work demonstrates that $N$-body systems with two-body zero-range interactions can be treated reliably and efficiently by the finite temperature and ground state path integral Monte Carlo approaches, using the exact two-body propagator for zero-range interactions in the pair product approximation. The performance of the propagators is tested by reproducing known results for various one- and three-dimensional systems. We further calculate the energy and structural properties for the ground state of $N$ three-dimensional bosons at unitary interacting via two-body zero-range and three-body repulsive potentials.