Dynamical mean-field theory of electron-phonon interaction in correlated   electron materials: general results and application to doped Mott insulators
  The dynamical mean-field method is used to formulate a computationally tractable theory of electron-phonon interactions in systems with arbitrary local electron-electron interactions in the physically relevant adiabatic limit of phonon frequency small compared to electron bandwidth or interaction scale. As applications, the phonon contribution to the effective mass of a carrier in a lightly doped Mott insulator is determined and the phase separation boundary is discussed. 
A. Deppeler and A. J. Millis