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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 ofthe two-dimensional metal are presented. In various dimensions D, it is foundanalytically and numerically that the density matrix decays with distanceaccording to the power law, $+AFw-rho({+AFw-bf r},{+AFw-bf r^+AFw-prime})+AFw-propto |{+AFw-bf r}-{+AFw-bf r^+AFw-prime}|^{-(D+-1)/2}$.Comment: 4 pages, 5 figure

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