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Correlation effects and the high-frequency spin susceptibility of an electron liquid: Exact limits

G. S. Atwal·N. W. Ashcroft
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Abstract

Spin correlations in an interacting electron liquid are studied in the high-frequency limit and in both two and three dimensions. The third-moment sum rule is evaluated and used to derive exact limiting forms (at both long- and short-wavelengths) for the spin-antisymmetric local-field factor, $\lim_{ω\to \infty}G_-({\bf q, ω})$. In two dimensions $\lim_{ω\to \infty}G_-({\bf q, ω})$ is found to diverge as $1/q$ at long wavelengths, and the spin-antisymmetric exchange-correlation kernel of time-dependent spin density functional theory diverges as $1/q^2$ in both two and three dimensions. These signal a failure of the local-density approximation, one that can be redressed by alternative approaches.

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G. S. Atwal, N. W. Ashcroft. 2003-05-08. Correlation effects and the high-frequency spin susceptibility of an electron liquid: Exact limits. https://doi.org/10.1103/physrevb.67.233104

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