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We calculate the momentum dependent spectral function of the Bose-Hubbardmodel on a simple cubic lattice in three dimensions within the bosonicdynamical mean-field theory (B-DMFT). The continuous-time quantum Monte Carlomethod is used to solve the self-consistent B-DMFT equations together with themaximum entropy method for the analytic continuation to real frequencies.Results for weak, intermediate, and strong interactions are presented. In thelimit of weak and strong interactions very good agreement with results obtainedby perturbation theory is found. By contrast, at intermediate interactions theresults differ significantly, indicating that in this regime perturbativemethods fail do describe the dynamics of interacting bosons.

Numerical calculation of spectral functions of the Bose-Hubbard model using B-DMFT