HOLSTEIN MODEL IN INFINITE DIMENSIONS

Monte Carlo simulations are performed to examine superconductivity and charge-density-wave fluctuations in the infinite-dimensional electron -phonon Holstein model. The electron-phonon system interpolates betwee n an attractive, static, Falicov-Kimball model that always exhibits ch arge-density-wave order and an attractive, instantaneous, Hubbard mode l that always superconducts as a function of phonon frequency. The max imum charge-density-wave transition temperature at half-filling is an order of magnitude smaller than the effective electronic bandwidth and is virtually independent of the phonon frequency. The maximum superco nducting transition temperature depends strongly on phonon frequency a nd is bounded from above by the maximum charge-density-wave transition temperature. The exact solution is compared to both weak-coupling exp ansions and strong-coupling expansions. The effective phonon potential becomes anharmonic and develops a double-well structure that deepens as the electron-phonon interaction increases.