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 as and temperature T. This is done by improving a one-loop result near the interaction-free Bose-Einstein critical temperature Tc(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 Tc(0), so that we predict the existence of a reentrant transition above Tc(0), where an increasing repulsion leads to the formation of a condensate.

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