We reexamine the Brandt-Mielsch solution of the Falicov-Kimball model in infinite dimensions, to elucidate the mechanism for the breakdown of Fermi-liquid theory in this model. We find that this breakdown is due to the pinning of the chemical potential at the localized particle level. When this pinning does not occur, Fermi-liquid theory is restored. Using a Lorentzian density of states, we obtain analytic expressions for spectral densities and local response functions. These expressions give new insights into the formation of upper and lower Hubbard bands, the metal-insulator transition, the softening of the collective modes, and the infrared singularities of this model.

• Received 5 November 1991

DOI:https://doi.org/10.1103/PhysRevB.46.1261