Strong coupling expansion for the Bose-Hubbard and Jaynes-Cummings lattice models

A strong coupling expansion based on the Kato-Bloch perturbation theory, which has recently been proposed by Eckardt et?al (2009 Phys. Rev. B 79 195131) and Teichmann et?al (2009 Phys. Rev. B 79 224515), is implemented in order to study various aspects of the Bose-Hubbard and Jaynes-Cummings lattice models. The approach, which allows us 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 Jaynes-Cummings lattice models will be presented and compared with results from the variational cluster approach and density matrix renormalization group. Our focus will be on the Mott insulator to superfluid transition.