Degenerate ground states and nonunique potentials: Breakdown and restoration of density functionals
- Departamento de Fisica e Informatica, Instituto de Fisica de Sao Carlos, Universidade de Sao Paulo, Caixa Postal 369, 13560-970 Sao Carlos, SP (Brazil)
- Department of Physics and Astronomy, University of Missouri-Columbia, Columbia, Missouri 65211 (United States)
The Hohenberg-Kohn (HK) theorem is one of the most fundamental theorems of quantum mechanics, and constitutes the basis for the very successful density-functional approach to inhomogeneous interacting many-particle systems. Here we show that in formulations of density-functional theory (DFT) that employ more than one density variable, applied to systems with a degenerate ground state, there is a subtle loophole in the HK theorem, as all mappings between densities, wave functions, and potentials can break down. Two weaker theorems which we prove here, the joint-degeneracy theorem and the internal-energy theorem, restore the internal, total, and exchange-correlation energy functionals to the extent needed in applications of DFT to atoms, molecules, and solids. The joint-degeneracy theorem constrains the nature of possible degeneracies in general many-body systems.
- OSTI ID:
- 21011212
- Journal Information:
- Physical Review. A, Vol. 76, Issue 1; Other Information: DOI: 10.1103/PhysRevA.76.012508; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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