Reentrant Phenomenon in Quantum Phase Diagram of Optical Boson Lattice

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We calculate the location of the quantum phase transitions of a bose gas trapped in an optical lattice as a function of effective scattering length a and temperature T. Knowledge of recent high-loop results on the shift of the critical temperature at weak couplings is used to locate a nose in the phase diagram above the free Bose-Einstein critical temperature Tc⁽⁰⁾, thus predicting the existence of a reentrant transition above Tc⁽⁰⁾, where a condensate should form when increasing a. At zero temperature, the transition to the normal phase produces the experimentally observed Mott insulator.