Simulation of the electron-phonon interaction in infinite dimensions

The electron-phonon interaction corresponding to the Holstein model (with Coulomb repulsion) is simulated in infinite dimensions using a novel quantum Monte Carlo algorithm. The thermodynamic phase diagram includes commensurate charge-density-wave phases, incommensurate charge-density-wave phases, and superconductivity. The crossover from a weak-coupling picture (where pairs both form and condense at $T_c$) to a strong-coupling picture (where preformed pairs condense at $T_c$) is illustrated with the onset of a double-well structure in the effective phonon potential.