We investigate the properties of liquid \(^4\) He in both the normal and superfluid phases using path-integral Monte Carlo simulations and recently developed ab initio potentials that incorporate pair, three-body, and four-body interactions. By focusing on the energy per particle as a representative observable, we use a perturbative approach to quantify the individual contributions of the many-body potentials and systematically propagate their associated uncertainties. Our findings indicate that the three-body and four-body potentials contribute to the total energy by approximately 4% and 0.5%, respectively. However, the primary limitation in achieving highly accurate first principles calculations arises from the uncertainty in the four-body potential, which currently dominates the propagated uncertainty. In addition to the energy per particle, we analyze other key observables, including the superfluid fraction, condensed fraction, and pair distribution function, all of which demonstrate excellent agreement with experimental measurements.
