ZhETF, Vol. 143,
No. 4,
p. 729 (April 2013)
(English translation  JETP,
Vol. 116, No. 4,
p. 635,
April 2013
available online at www.springer.com
)
THE PROBLEM OF THE UNIVERSAL DENSITY FUNCTIONAL AND THE DENSITY MATRIX FUNCTIONAL THEORY
Bobrov V.B., Trigger S.A.
Received: October 4, 2012
DOI: 10.7868/S0044451013040125
The analysis in this paper shows that the HohenbergKohn theorem is the constellation of two statements: i) the mathematically rigorous HohenbergKohn lemma, which demonstrates that the same groundstate density cannot correspond to two different potentials of an external field, and ii) the hypothesis of the existence of the universal density functional. Based on the obtained explicit expression for the nonrelativistic particle energy in a local external field, we prove that the energy of the system of more than two noninteracting electrons cannot be a functional of the inhomogeneous density. This result is generalized to the system of interacting electrons. It means that the HohenbergKohn lemma cannot provide justification of the universal density functional for fermions. At the same time, statements of the density functional theory remain valid when considering any number of noninteracting groundstate bosons due to the Bose condensation effect. In the framework of the density matrix functional theory, the hypothesis of the existence of the universal density matrix functional corresponds to the cases of noninteracting particles and to interaction in the HartreeFock approximation.

