Spatial decay of the single-particle density matrix in tight-binding metals: Analytic results in two dimensions

Analytical results for the asymptotic spatial decay of the density matrix p(r,r') in the tight-binding model of the two-dimensional metal are presented. In various dimensions D, it is found analytically and numerically that the density matrix decays with distance according to the power law ρ(r,r')‖r-r'‖ - ( D + 1 ) / 2 .