Parity-projected resonating Hartree-Fock approximation to the Lipkin model

An exact eigenstate of the Lipkin-model Hamiltonian has a parity-symmetry. The resonating Hartree-Fock (Res-HF) ground-state wave function however bre aks the parity-symmetry. To restore the parity-symmetry, we develop at pari ty-projected (P-P) Res-HF approximation to the Lipkin model. The P-P Res-HF wave function is superposed by two P-P Slater determinants. Self-consisten t calculation is carried out so as to optimize the P-P Res-HF energy functi onal. A Res-HF ground state with definite parity brings us the ground-state energy much nearer to the exact one than that the Res-HF and explains most of the ground-state correlation energy. We also show behaviour of P-P Res- HF orbital energies and mixing coefficients calculated. by the P-P Res-UP a pproximation and compare them with those calculated by the parity-unproject ed Res-HF approximation. From this comparison, we find very interesting rel ations between them which have never been seen in the parity-unprojected Re s-HF calculation.