Application of the resonating Hartree-Fock theory to the Lipkin model

Abstract

In order to make clear essential features of the resonating Hartree-Fock (Res-HF) theory for a fermion system with large quantum fluctuations and to show its superiority over the usual HF theory, we apply it to the exactly solvable Lipkin model. We use a new direct-optimization algorithm to optimize orbitals in non-orthogonal Slater determinants (S-dets) in a Res-HF wave function. For our sake of simplicity, we assume a Res-HF wave function to be superposed by two S-dets | g 1〉 and | g 2〉 which give two corresponding local energy minima of monopole “deformation”. We make the self-consistent Res-HF calculation so as to minimize the energy functional including up to the second-order variation. The Res-HF ground state generated with only two S-dets brings us the ground-state energy very near to the exact one and then explains most of the ground-state correlation energy.