Dynamical Charge Susceptibility of the Spinless Falicov-Kimball Model

An exact solution is presented for the frequency-dependent charge susceptibility of the spinless Falicov-Kimball model by using dynamical mean-field theory. We develop a nontrivial application of the Baym-Kadanoff "conserving approximation" formalism to exactly determine the frequency-dependent vertex function (which turns out to assume a particularly simple form). We show how the static and dynamic susceptibilities are decoupled in this model and how the dynamic susceptibility generically does not show any signal of the low-temperature charge-density-wave phase transition. We also examine the temperature evolution of the dynamic charge susceptibility for the special case of half-filling.