Hohenberg-Kohn Theorems in the Presence of Magnetic Field
2014 (English)In: International Journal of Quantum Chemistry, ISSN 0020-7608, E-ISSN 1097-461X, Vol. 114, no 12, 782-795 p.Article in journal (Refereed) Published
In this article, we examine Hohenberg-Kohn theorems for Current Density Functional Theory, that is, generalizations of the classical Hohenberg-Kohn theorem that includes both electric and magnetic fields. In the Vignale and Rasolt formulation (Vignale and Rasolt, Phys. Rev. Lett. 1987, 59, 2360), which uses the paramagnetic current density, we address the issue of degenerate ground states and prove that the ensemble-representable particle and paramagnetic current density determine the degenerate ground states. For the formulation that uses the total current density, we note that the proof suggested by Diener (Diener, J. Phys.: Condens. Matter. 1991, 3, 9417) is unfortunately not correct. Furthermore, we give a proof that the magnetic field and the ensemble-representable particle density determine the scalar and vector potentials up to a gauge transformation. This generalizes the result of Grayce and Harris (Grayce and Harris, Phys. Rev. A 1994, 50, 3089) to the case of degenerate ground states. We moreover prove the existence of a positive wavefunction that is the ground state of infinitely many different Hamiltonians.
Place, publisher, year, edition, pages
John Wiley & Sons, 2014. Vol. 114, no 12, 782-795 p.
current density functional theory, Hohenberg– Kohn theorem, degeneracy, magnetic field
Mathematics Chemical Sciences
Research subject Mathematics
IdentifiersURN: urn:nbn:se:kth:diva-145534DOI: 10.1002/qua.24668ISI: 000335202500004ScopusID: 2-s2.0-84899983619OAI: oai:DiVA.org:kth-145534DiVA: diva2:718611
QC 201405232014-05-212014-05-212014-06-09Bibliographically approved