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Use of localized canonical solutions of the Hartree--Fock equations in many- body perturbation theory

Eytan Domany, Jacob Katriel, C.G. Kuper

Published Jan 1, 1975• 0 citations
OpenAlex

Abstract

The existence of localized canonical solutions of the Hartree--Fock equations is investigated. Application of a prescription proposed by Davidson provides the modification needed to settle the difficulties investigated by Brandow in the context of the theory of solid $sup 3$He.

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Progress of Theoretical Physics•Jan 1, 1984•4 citations
The existence of localized canonical solutions of the Hartree--Fock equations is investigated. Application of a prescription proposed by Davidson provides the modification needed to settle the difficulties investigated by Brandow in the context of the theory of solid sup3sup 3sup3He.
The question of the possible existence of localized canonical Hartree-Fock (HF) eigenfunctions in periodic systems is more subtle than has generally been recognized. The first analysis of this issue, by Kaplan and Argyres, is shown to be incomplete and thus inconclusive. We present a new argument which shows conclusively that localized canonical HF solutions cannot exist in periodic systems of physical interest. Other arguments, with varying emphasis on symmetry, intuition, and formal rigor, are also discussed. Consequences of this result for the understanding of Mott insulators will be discussed elsewhere.
A necessary condition for the stability of the Hartree-Fock solution in many-body problem is presented. If this condition is not satisfied, then the solution becomes no longer stable as was discussed by Overhauser in connection with the one-dimensional spin wave model. A variational method is proposed in this case to construct a stable solution which has definitely a lower energy than the Hartree-Fock value. The workability of our method is tested in some realistic examples like the B.C.S.-Bogolyubov theory of superconductivity. Then the method is applied to field theory which seems to be inconsistent in view of the presence of “ghost states”. A canonical transformation leads to a new vacuum state with lower energy, but the high momentum part of the coupling is not damped.