Exact exchange and correlation corrections for large wave vectors

Abstract

We extend Niklasson's method in order to study the spin response of an electron liquid in a weak sinusoidal magnetic field. The many-body correction $G-(\overrightarrow{\mathrm{q}},\omega )$ caused by exchange and correlation is introduced to describe the correct wave-vector- and frequency-dependent spin susceptibility. The exact behavior of $G-(\overrightarrow{\mathrm{q}},\omega )$ in the large-$q$ limit is related to the pair distribution function $g\left(\overrightarrow{\mathrm{r}}\right)$ at $r=0\mathrm{}$. $G_{-}(\overrightarrow{\mathrm{q}},\omega )\to \frac{\mathrm{}\left[4g\right(0)-1]}{3}$, as $q\to \infty$. At metallic densities this value is negative, opposite in sign to the limit at small wave vector. Thus the spin susceptibility for large wave vectors is suppressed, rather than enhanced, by many-body effects.