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

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, $\lim_{\omega \to \infty}G_-({\bf q, \omega})$. In two dimensions $\lim_{\omega \to \infty}G_-({\bf q, \omega})$ 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.