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

TL;DR

This paper analytically investigates how the single-particle density matrix decays with distance in two-dimensional tight-binding metals, revealing a universal power-law decay behavior across different dimensions.

Contribution

It provides the first analytical derivation of the asymptotic decay of the density matrix in 2D tight-binding metals, confirming numerical results and extending understanding across dimensions.

Findings

Density matrix decays as a power law with distance in 2D metals.

Analytical and numerical results agree on decay behavior.

Decay exponent depends on the spatial dimension D.

Abstract

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, $+AFw-rho({+AFw-bf r},{+AFw-bf r^+AFw-prime}) +AFw-propto |{+AFw-bf r}-{+AFw-bf r^+AFw-prime}|^{-(D+-1)/2}$.