Strong interaction of correlated electrons with phonons: A diagrammatic approach

We investigate the interaction of strongly correlated electrons with phonon s in the frame of the Hubbard-Holstein model. The electron-phonon interacti on is considered to be strong and is an important parameter of the model be sides the Coulomb repulsion of electrons and band filling. This interaction with the nondispersive optical phonons has been transformed to the problem of mobile polarons by using the canonical transformation of Lang and Firso v. A new diagram technique is used in order to handle the strong Coulomb re pulsion of the electrons, which leads to a closed set of integral equations for the irreducible on-site many-particle Green's functions. The coupling to the phonons leads to an essential renormalization of the one- and two-pa rticle irreducible Green's functions. It also influences the parameters whi ch control the metal-insulator or superconducting phase transition. In addi tion we find a collective mode of phonon clouds which surround the polarons . The physics of the emission and absorption of this mode by the polarons h as been investigated. [S0163-1829(99)12801-7].