Quantum criticality of a Bose gas in an optical lattice near the Mott transition

We derive the equation of state of bosons in an optical lattice in the framework of the Bose-Hubbard model. Near the density-driven Mott transition, the expression of the pressure P(mu, T) versus chemical potential and temperature is similar to that of a dilute Bose gas but with renormalized mass m* and scattering length a*. Here m* is the mass of the elementary excitations at the quantum critical point governing the transition from the superfluid phase to the Mott-insulating phase, while a* is related to their effective interaction at low energy. We use a nonperturbative renormalization-group approach to compute these parameters as a function of the ratio t/U between hopping amplitude and on-site repulsion.