Abstract
We calculate the dielectric function of the lattice Anderson model via an auxiliary-boson large-N method suitably generalized to include the effects of the long-range part of the Coulomb interaction. We show that the model exhibits a low-lying plasma oscillation at a frequency \ensuremath{\omega} on the order of the Kondo temperature of the model, in addition to the usual high-frequency plasma oscillation. We also analyze the Anderson model without the long-range Coulomb interaction, computing the Landau parameter ${F}_{0s}$, and showing that the model has a zero-sound mode whose velocity we compute. We derive the version of the f sum rule applicable to our model and show that our results satisfy it.
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