Numerical calculation of spectral functions of the Bose-Hubbard model using bosonic dynamical mean-field theory

We calculate the momentum dependent spectral function of the Bose-Hubbard model on a simple cubic lattice in three dimensions within the bosonic dynamical mean-field theory (B-DMFT). The continuous-time quantum Monte Carlo method is used to solve the self-consistent B-DMFT equations together with the maximum entropy method for the analytic continuation to real frequencies. Results for weak, intermediate, and strong interactions are presented. In the limit of weak and strong interactions very good agreement with results obtained by perturbation theory is found. By contrast, at intermediate interactions the results differ significantly, indicating that in this regime perturbative methods fail to describe the dynamics of interacting bosons.