Absence of proof for the Hohenberg–Kohn theorem for a Hamiltonian linear in the magnetic field
Savin , Andreas
- Publisher: Taylor & Francis
magnetic fields | Density functional theory | [ PHYS ] Physics [physics]
arxiv: Physics::Chemical Physics
International audience; 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 i) not only the spin-dependent, but also the orbital-dependent term should be taken care of, and ii) the latter produces eigenvalues that are not bounded from below, thus invalidating the proof of the Hohenberg-Kohn theorem.