Spatial decay of the single-particle density matrix in insulators: analytic results in two and three dimensions

Analytic results for the asymptotic decay of the electron density matrix in insulators have been obtained in all three dimensions ($D=1 - 3$) for a tight-binding model defined on a simple cubic lattice. The anisotropic decay length is shown to be dependent on the energy parameters of the model. The existence of the power-law prefactor, $+AFw-propto r^{-D/2}$, is demonstrated.