N-representability in noncollinear spin-polarized density-functional theory

The N-representability problem for noncollinear spin-polarized densities was left open in the pioneering work of von Barth and Hedin setting up the Kohn-Sham density-functional theory for magnetic compounds. In this Letter, we demonstrate that, contrarily to the nonpolarized case, the sets of pure and mixed state N-representable densities are different in general. We provide a simple characterization of the latter by means of easily checkable necessary and sufficient conditions on the components ραβ(r) of the spin-polarized density.