Absence of proof for the Hohenberg–Kohn theorem for a Hamiltonian linear in the magnetic field

ABSTRACT

The widespread idea that spin-density functional theory is based upon the extension of the Hohenberg–Kohn theorem to weak magnetic fields is contested. First, it is assumed that only the term linear in magnetic field can be kept in the Hamiltonian. Second, once this is done, two problems arise (1) not only the spin-dependent, but also the orbital-dependent term should be taken care of, and (2) the latter produces eigenvalues that are not bounded from below, thus invalidating the proof of the Hohenberg–Kohn theorem.

KEYWORDS:

• Density functional theory
• magnetic fields

Acknowledgments

This paper is dedicated to Hans Jørgen Aagaard Jensen, in continuation to our enjoyable discussions on the meaning of spin-density functional theory, and its extension to multi-configuration methods.

Disclosure statement

No potential conflict of interest was reported by the author.