$N$-representability in non-collinear spin-polarized density functional theory

摘要

The $N$-representability problem for non-collinear spin-polarized densitieswas left open in the pioneering work of von Barth and Hedin setting up theKohn-Sham density functional theory for magnetic compounds. In this letter, wedemonstrate that, contrarily to the non-polarized case, the sets of pure andmixed state $N$-representable densities are different in general. We provide asimple characterization of the latter by means of easily checkable necessaryand sufficient conditions on the components $\rho^{\alpha \beta} (\br)$ of thespin-polarized density.