Symmetry-projected Hartree–Fock–Bogoliubov equations

Abstract

Symmetry-projected Hartree–Fock–Bogoliubov (HFB) equations are derived using the variational ansatz for the generalized one-body density matrix in the Valatin form. It is shown that the projected-energy functional can be completely expressed in terms of the HFB density matrix and the pairing-tensor. The variation of this projected energy is shown to result in HFB equations with modified expressions for the pairing-potential Δ and the Hartree–Fock field Γ. The expressions for these quantities are explicitly derived for the case of particle number projection. The numerical applicability of this projection method is studied in an exactly soluble model of a deformed single-j shell.