Spatial decay of the single-particle density matrix in tight-binding   metals: +AFwAXA- analytic results in two dimensions
  Analytical results for the asymptotic spatial decay of the density matrix $+AFw-rho({+AFw-bf r},{+AFw-bf r^+AFw-prime})$ 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, $+AFw-rho({+AFw-bf r},{+AFw-bf r^+AFw-prime}) +AFw-propto |{+AFw-bf r}-{+AFw-bf r^+AFw-prime}|^{-(D+-1)/2}$. 
S.N. Taraskin, P.A. Fry, Xiadong Zhang, D.A. Drabold and S.R. Elliott