Linear and nonlinear optical characteristics of the Falicov-Kimball model

We calculate the linear and nonlinear optical properties of the Falicov-Kimball model for a mixed-valent system within the self-consistent mean-field approximation. Second-harmonic generation can only occur if the mixed-valent state has a built-in coherence between the itinerant d electrons and the localized f holes. By contrast, second-harmonic generation cannot occur for solutions of the model with f-site occupation as a good quantum number. As an experimental test of coherence in mixed-valent compounds we propose a measurement of the dynamic second-order susceptibility.