Properties of the density matrix from realistic calculations

We compute the single particle density matrix in large (500, 512 and 1000 atom) models of FCC aluminum, crystalline (diamond) and amorphous silicon and carbon. We use an approximate density functional Hamiltonian in the local density approximation. The density matrix for FCC aluminum is found to closely approximate the results for jellium, and the crystalline and amorphous insulators exhibit exponential decay albeit with pronounced anisotropy. We compare the computed decays to existing predictions of the fall o of the density matrix in insulators and nd that the \tight-binding" prediction of Kohn [W. Kohn, Phys. Rev. 115 809 (1959)] provides the best overall t to our calculations for Si and C. Typeset using REVTEX