Electron-phonon interaction in strongly correlated systems

Abstract

By a canonical transformation, the Hubbard model, supplemented with the Holstein interaction of localized electrons and nondispersive optical phonons, is transformed into a model where the hoppings of polarons from one lattice site into another are possible and are accompanied by the hoppings of an unbounded number of phonons. This, together with the fact that strong one-site interactions of electrons are inherent in the Hubbard model, leads to the necessity of introducing a new diagram technique based on irreducible one-site multi-particle Green’s functions or Kubo cumulants. The presence of phonons leads to renormalization of single-particle and multi-particle Green’s functions. The Dyson equation for the renormalized electron Green’s function is obtained. However, we did not manage to obtain the Dyson equation for the phonon functions due to the multiplicity of phonons taking part in the hopping. The validity of the theorem of connected diagrams is proved.