We present a nonperturbative renormalization group (RG) approach to the Bose-Hubbard model. By taking as initial condition of the RG flow the (local) limit of decoupled sites, we take into account both local and long-distance fluctuations in a nontrivial way. This approach yields a phase diagram in very good quantitative agreement with the quantum Monte Carlo results and reproduces the two universality classes of the superfluid–Mott-insulator transition with a good estimate of the critical exponents. Furthermore, it reveals the crucial role of the “Ginzburg length” as a crossover length between a weakly and a strongly correlated superfluid phase.

• Received 18 February 2011

DOI:https://doi.org/10.1103/PhysRevB.83.172501