Strong-coupling theory for the Hubbard model

We reanalyze the Hubbard-I approximation by showing that it is equivalent t o an effective Hamiltonian describing Fermionic charge fluctuations, which can be solved by Bogoliubov transformation. As the most important correctio n in the limit of large U and weak spin correlations we augment this Hamilt onian by further effective particles, which describe composite objects of a Fermionic charge fluctuation and a spin-, density-, or eta excitation. The scheme is valid for positive and negative U. We present results for the si ngle particle Green's function for the two-dimensional Hubbard model with a nd without t' and t " terms, and compare to quantum Monte-Carlo results for the paramagnetic phase. The overall agreement is significantly improved ov er the conventional Hubbard-I or two-pole approximation.