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, $+AFw-rho({+AFw-bf r},{+AFw-bf r^+AFw-prime}) +AFw-propto |{+AFw-bf r}-{+AFw-bf r^+AFw-prime}|^{-(D+-1)/2}$.
Source: http://arxiv.org/abs/cond-mat/0207443v2