Schwinger representation approach to the Lipkin model

The Schwinger representation and the Marumori–Yamamura–Tokunaga boson expansion are used to describe the Lipkin model in terms of generalized coherent states. The groundstate, first excited state and RPA energies are obtained within several variant types of coherent states. It has been found that generalized coherent states defined in consonance with the parity symmetry of the model describe particularly well the transition from weak to strong coupling, providing a remarkable improvement of the mean-field description of the transition zone.