  We work out two different analytical methods for calculating the boundary of
the Mott-insulator-superfluid (MI-SF) quantum phase transition for scalar
bosons in cubic optical lattices of arbitrary dimension at zero temperature
which improve upon the seminal mean-field result. The first one is a
variational method, which is inspired by variational perturbation theory,
whereas the second one is based on the field-theoretic concept of effective
potential. Within both analytical approaches we achieve a considerable
improvement of the location of the MI-SF quantum phase transition for the first
Mott lobe in excellent agreement with recent numerical results from Quantum
Monte-Carlo simulations in two and three dimensions. Thus, our analytical
results for the whole quantum phase diagram can be regarded as being
essentially exact for all practical purposes.
