  A strong coupling expansion, based on the Kato-Bloch perturbation theory,
which has recently been proposed by Eckardt et al. [Phys. Rev. B 79, 195131]
and Teichmann et al. [Phys. Rev. B 79, 224515] is implemented in order to study
various aspects of the Bose-Hubbard and the Jaynes-Cummings lattice model. The
approach, which allows to generate numerically all diagrams up to a desired
order in the interaction strength is generalized for disordered systems and for
the Jaynes-Cummings lattice model. Results for the Bose-Hubbard and the
Jaynes-Cummings lattice model will be presented and compared with results from
VCA and DMRG. Our focus will be on the Mott insulator to superfluid transition.
