Electron - phonon interaction in strongly correlated systems. Acoustical phonon case

Abstract

We investigate the interaction of strongly correlated electrons with acoustical phonons in the frame of Hubbard-Holstein model. The electron-phonon interaction and on-site Coulomb repulsion are considered to be strong. By using the Lang-Firsov canonical transformation this problem has been transformed to the problem of mobile polarons. A new diagram technique is used in order to handle the strong Coulomb repulsion of the electrons and the existence of phonon clouds surrounding the electrons. The generalized Wick theorems for chronological products of electron and phonon-clouds operators have been formulated. We have found the collective mode of phonon clouds that surround electrons and discussed the physics of the emission and absorption of this mode by the polarons. We have also discussed the difference in the behaviour of optical and acoustical phonon-clouds surrounding polarons during their movement through the crystal lattice.