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

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, ${\lim }_{\omega \to \infty }{G}_{-}(\mathbf{q},\omega )$. In two dimensions ${\lim }_{\omega \to \infty }{G}_{-}(\mathbf{q},\omega )$ 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.

arXiv comment5 pages

References in corpus (6)

• Current-dependent exchange-correlation potential for dynamical linear response theory
• Time-dependent density functional theory beyond the adiabatic local density approximation
• Analytical expressions for the local-field factor G(q) and the exchange-correlation kernel K_{xc}(r) of the homogeneous electron gas
• Analytical expressions for the charge-charge local-field factor and the exchange-correlation kernel of a two-dimensional electron gas
• Many-body GW Calculations of Ground-State Properties: Quasi-2D Electron Systems and van der Waals Forces
• Analytical expressions for the spin-spin local-field factor and the spin-antisymmetric exchange-correlation kernel of a two-dimensional electron gas

Cited by in corpus (3)

• Pair-distribution functions of the two-dimensional electron gas
• Long wavelength behavior of the dynamical spin-resolved local-field factor in a two-dimensional electron liquid
• Correlation induced out-of-phase plasmon in an electron liquid