Degenerate ground states and nonunique potentials: breakdown and restoration of density functionals

Details Degenerate ground states and nonunique potentials: breakdown and restoration of density functionals Degenerate ground states and nonunique potentials: breakdown and restoration of density functionals

2006-10-11

arxiv.org/abs/cond-mat/0610322v1

Phys. Rev. A 76, p. 012508 (2007)

Physics

Condensed Matter

Materials Science

Scientific paper

10.1103/PhysRevA.76.012508

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 atomic, molecular and solid-state physics and quantum chemistry. The joint-degeneracy theorem constrains the nature of possible degeneracies in general many-body systems.

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