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

TL;DR

It is demonstrated that, contrarily to the nonpolarized case, the sets of pure and mixed state N-representable densities are different in general.

Abstract

The $N$-representability problem for non-collinear 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 non-polarized 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 $ρ^{αβ} (\br)$ of the spin-polarized density.

Theorems & Definitions (4)

• Theorem 1
• Corollary 1
• proof : Proof of Theorem 1
• proof : Proof of Corollary 1