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 and 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 off of the density matrix in insulators and find that the ``tight-binding'' prediction of Kohn [W. Kohn, Phys. Rev. 115, 809 (1959)] provides the best overall fit to our calculations for Si and C.