Pure-state $N$-representability in current-spin-density-functional theory

TL;DR

This paper investigates the conditions under which certain spin-density matrices and paramagnetic currents can be represented by Slater determinants in current-spin-density-functional theory, focusing on systems with magnetic fields.

Contribution

It provides necessary and sufficient conditions for pure-state $N$-representability of spin-density matrices and sufficient conditions for currents, advancing the theoretical understanding in magnetic systems.

Findings

Necessary and sufficient conditions for $R$ to be Slater-representable.

Sufficient conditions on $ extbf{j}$ for $(R, extbf{j})$ to be Slater-representable for $N > 12$.

Open problem for $N < 12$ cases.

Abstract

This paper is concerned with the pure-state $N$-representability problem for systems under a magnetic field. Necessary and sufficient conditions are given for a spin-density $2 \times 2$ matrix $R$ to be representable by a Slater determinant. We also provide sufficient conditions on the paramagnetic current $\mathbb{j}$ for the pair $(R, \mathbb{j})$ to be Slater-representable in the case where the number of electrons $N$ is greater than 12. The case $N < 12$ is left open.