Random-phase approximation approach to rotational symmetry restoration in a three-level Lipkin model

We study an extended Lipkin-Meshkov-Glick model that permits a transition to a deformed phase with a broken continuous symmetry. Unlike simpler models, one sees a persistent zero-frequency Goldstone mode past the transition point into the deformed phase. We found that the RPA formula for the correlation energy provides a useful correction to the Hartree-Fock energy when the number of particle N satisfies $N>\mathrm{}3,$ 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 energies.