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Physical Review A

Nondeterminantal Hartree-Fock theory

George Rosensteel, DAVID J. ROWE

Published Aug 1, 1981• 32 citations
Publisher

Abstract

Hartree-Fock (HF) theory is generalized so as to apply to nondeterminantal densities, while retaining the fundamental HF restriction to one-body dynamics. Time development in conventional time-dependent Hartree-Fock and its extension are identical to classical Hamiltonian dynamics.
DOI
10.1103/physreva.24.673

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Hartree-Fock-Bogoliubov (HFB) theory is generalized by eliminating the restriction to quasiparticle vacuum states. However, the fundamental HFB transformation to quasiparticles is retained. The theory is formulated in terms of the quasiparticle density matrix RRR, but, in contrast to conventional HFB, there is no restriction to vacuum densities R2=R{R}^{2}=RR2=R.
We show that to any Lie algebra of observables in quantum mechanics there corresponds a system of densities, of which the one-body densities are just one example. These densities may correspond to a single pure state or to an ensemble of states. Like the one-body densities, they support a Hamiltonian dynamics of the time-dependent Hartree-Fock type, which can be applied, for example, to collective motions where the collective states of interest may be either more or less general than single Slater determinants. The dynamics can also be applied to the average dynamics of an ensemble of states.
The variational derivation of the time-dependent Hartree-Fock equation is reviewed. When norm-violating variations are included, a unique time-dependent Hartree-Fock Hamiltonian, which differs from that customarily used in time-dependent Hartree-Fock analyses, is implied. This variationally "true" Hartree-Fock Hamiltonian has the same expectation value as the exact Hamiltonian, equal to the average energy of the system. Since this quantity remains constant under time-dependent Hartree-Fock time evolution, we suggest the label "constant 〈H〉〈H〉〈H〉" for this form of time-dependent Hartree-Fock theory.NUCLEAR REACTIONS Unique time-dependent Hartree-Fock Hamiltonian obtained from variational principle by norm-violating variations.