New boson realization of the Lipkin model obeying the su(2)-algebra

TL;DR

This paper introduces a new boson representation of the su(2)-algebra tailored for the Lipkin model, enabling effective description across various fermion numbers, with potential applications in many-fermion systems.

Contribution

The authors propose a novel boson realization of the su(2)-algebra using two bosons and a third to handle any fermion number, extending previous models.

Findings

The new representation accurately models the Lipkin system.

It is effective for any fermion number.

The approach simplifies the bosonization of many-fermion models.

Abstract

New boson representation of the su(2)-algebra proposed by the present authors for describing the damped and amplified oscillator is examined in the Lipkin model as one of simple many-fermion models. This boson representation is expressed in terms of two kinds of bosons with a certain positive parameter. In order to describe the case of any fermion number, third boson is introduced. Through this examination, it is concluded that this representation is well workable for the boson realization of the Lipkin model in any fermion number.