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In this article, we consider quantum crystals with defects in the reducedHartree-Fock framework. The nuclei are supposed to be classical particlesarranged around a reference periodic configuration. The perturbation is assumedto be small in amplitude, but need not be localized in a specific region ofspace or have any spatial invariance. Assuming Yukawa interactions, we provethe existence of an electronic ground state, solution of the self-consistentfield equation. Next, by studying precisely the decay properties of thissolution for local defects, we are able to expand the density of states of thenonlinear Hamiltonian of a system with a random perturbation ofAnderson-Bernoulli type, in the limit of low concentration of defects. Oneimportant step in the proof of our results is the analysis of the dielectricresponse of the crystal to an effective charge perturbation.

The reduced Hartree-Fock model for short-range quantum crystals with defects