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 ${(U∕t)}_{\mathrm{c}}=29.34(2)$, and the insulating gap $\ensuremath{\Delta}$ 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 $(T⪡\ensuremath{\Delta})$ 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.

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