The Electron-Phonon Problem in Infinite Dimensions

Monte Carlo simulations are performed to examine superconductivity and charge-density-wave fluctuations in the infinite-dimensional electron-phonon problem. The maximum charge-density-wave transition temperature is an order of magnitude smaller than the effective electronic bandwidth and is virtually independent of the phonon frequency. The maximum superconducting transition temperature depends strongly on phonon frequency and is bounded by the maximum charge-density-wave transition temperature. The crossover from weak to strong coupling is illustrated by the evolution of an effective phonon potential that develops a double-well structure as the electron-phonon interaction increases.