On an effective Hamiltonian that describes quasihomeopolar excitations in the framework of the Hubbard model

A graphical technique is constructed for calculating in perturbation theory the adiabatic $S$ matrix in the Hubbard model in the atomic limit. This graphical technique is used to prove a generalization of the connected graph theorem to the case when the $S$ matrix is restricted to the $2N$-dimensional homeopolar subspace ($N$ is the number of sites in the considered volume of the lattice). A direct consequence of this generalization is the existence of an effective Hamiltonian that describes quasihomeopolar excitations in the framework of the Hubbard model and does not contain volume divergences in any order in the coupling constant. Graphical rules are formulated for calculating this effective Hamiltonian.