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 = 1,2,3) 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, proportional, variant r(-D/2), is demonstrated.