Phase diagram and thermodynamics of the three-dimensional Bose-Hubbard model

We report results of quantum Monte Carlo simulations of the Bose-Hubbard model in three dimensions. Critical parameters for the superfluid-to-Mott-insulator transition are determined with significantly higher accuracy than has been done in the past. In particular, the position of the critical point at filling factor n=1 is found to be at (U∕t) ₂=29. 34 (2), and the insulating gap is measured with accuracy of a few percent of the hopping amplitude t. We obtain the effective mass of particle and hole excitations in the insulating state---with explicit demonstration of the emerging particle-hole symmetry and relativistic dispersion law at the transition tip---along with the sound velocity in the strongly correlated superfluid phase. These parameters are the necessary ingredients to perform analytic estimates of the low temperature (T⪡) thermodynamics in macroscopic samples. We present accurate thermodynamic curves, including these for specific heat and entropy, for typical insulating (U∕t=40) and superfluid (t∕U=0. 0385) phases. Our data can serve as a basis for accurate experimental thermometry, and a guide for appropriate initial conditions if one attempts to use interacting bosons in quantum information processing.