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

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, the authors apply it to the exactly solvable Lipkin model. They use a new direct optimization algorithm to optimize orbitals in nonorthogonal Slater determinants (S-dets) in a Res HF wave function. For the sake of simplicity, they assume a Res HF wave function to be superposed by two S-dets |g1> |g2> which give corresponding two local energy minima of monopole deformation. They 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 the ground state energy very near to the exact one and then explains most of the ground state correlation energy