Numerical study of Holstein's molecular-crystal model: Adiabatic limit and influence of phonon dispersion

We report on simulations for the molecular-crystal model without dispersion in the adiabatic regime for all lattice dimensionalities. A discrete version of the Feynman path-integral formalism is used to calculate the electron properties. We compare these results with approximate theories and conclude that continuum versions of the molecular-crystal model have little relationship to the discrete lattice model. In addition, the influence of the phonon dispersion on the transition between the "untrapped" and "self-trapped" state of an electron on a one-dimensional lattice is studied within the context of Holstein's molecular-crystal model. We show that the electron-phonon interaction has a critical value below which self-trapping does not occur. We find that this critical value goes to zero if the optical phonon becomes soft.