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

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 $\mathrm{j}$ for the pair $(R, \mathrm{j})$ to be Slater-representable in the case where the number of electrons $N$ is greater than $12$. The case $N \lt 12$ is left open.

Keywords

quantum theory, density functional theory, paramagnetic current, representability

2010 Mathematics Subject Classification

81Q05, 81V55

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Published 5 June 2023