Quantum phase diagram for homogeneous Bose‐Einstein condensate

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 based on 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.