  We calculate the quantum phase transition for a homogeneous Bose gas in the
plane of s-wave scattering length a_s and temperature T. This is done by
improving a one-loop result near the interaction-free Bose-Einstein critical
temperature T_c^{(0)} with the help of recent high-loop results on the shift of
the critical temperature due to a weak atomic repulsion using variational
perturbation theory. The quantum phase diagram shows a nose above T_c^{(0)}, so
that we predict the existence of a reentrant transition above T_c^{(0)}, where
an increasing repulsion leads to the formation of a condensate.
