Dynamical Mean Field Solution of the Bose-Hubbard Model

We present the effective action and self-consistency equations for the bosonic dynamical mean field approximation to the bosonic Hubbard model and show that it provides remarkably accurate phase diagrams and correlation functions. To solve the bosonic dynamical mean field equations, we use a continuous-time Monte Carlo method for bosonic impurity models based on a diagrammatic expansion in the hybridization and condensate coupling. This method is readily generalized to bosonic mixtures, spinful bosons, and Bose-Fermi mixtures.