Two-Level Lipkin Model in Unconventional Boson Realization

TL;DR

This paper proposes a novel two-level Lipkin model using an unconventional boson realization of the su(2) algebra, extending previous methods to open shell systems and generalizing RPA results.

Contribution

It introduces a new boson realization approach for the Lipkin model applicable to open shell systems, based on Schwinger and Holstein-Primakoff representations.

Findings

Proposes a boson realization for su(2) in Lipkin model

Provides an approximate form generalizing RPA results

Extends boson realization methods to open shell systems

Abstract

With the aim of applying to the Lipkin model in the case of open shell system, a possible form of the boson realization for the su(2)-algebra is proposed both in the Schwinger and the Holstein-Primakoff representation. The basic idea is borrowed from the Schwinger boson realization for the su(4)-algebra for many-quark system recently presented by the present authors. As the simplest approximation, a certain approximate form is given and the result is a natural generalization of the RPA result in the case of closed shell system.