Random-phase approximation approach to rotational symmetry restoration in a three-level Lipkin model - art. no. 024307

We study an extended Lipkin-Meshkov-Glick model that permits a transition t o a deformed phase with a broken continuous symmetry. Unlike simpler models , one sees a persistent zero-frequency Goldstone mode past the transition p oint into the deformed phase. We found that the RPA formula for the correla tion energy provides a useful correction to the Hartree-Fock energy when th e number of particle N satisfies N>3, and becomes accurate for large N. We conclude that the RPA correlation energy formula offers a promising way to improve the Hartree-Fock energy in a systematic theory of nuclear binding e nergies.