Electron-phonon interaction of strong correlated systems

The Hubbard–Holstein model after Canonical Lang–Firsov transformation is investigated. Two peculiarities of the model are taken into account: the strong electron correlations and the fact that the hopping of polarons between lattice sites are accompanied by an unrestricted number of phonons. A new diagram technique based on the classification of irreducible multi-particle Green functions is developed. A theorem about the Connected Vacuum diagrams is established and the Dyson equation for the electron Green functions is obtained.