Background of the su(2)-Algebraic Many-Fermion Models in the Boson Realization

TL;DR

This paper develops a unified su(2)-algebraic framework for understanding three fermion models, introducing an auxiliary algebra and boson realization to clarify their structures and behaviors.

Contribution

It introduces an auxiliary su(2)-algebra and boson realization to unify and analyze three key fermion models within a single algebraic framework.

Findings

Unified understanding of three fermion models achieved

Boson realization simplifies the structure of models

Distinct behavior of total fermion in Lipkin model

Abstract

The su(2)-algebraic many-fermion model is formulated so as to be able to get the unified understanding of the structures of three simple models: the single-level pairing, the isoscalar proton-neutron pairing and the two-level Lipkin model. Basic idea is to introduce an auxiliary su(2)-algebra, any generator of which commutes with any generator of the starting su(2)-algebra. With the aid of this algebra, the minimum weight states are completely determined in a simple forms. Further, concerning the two algebras, boson realization is presented. Through this formulation, the behavior of the total fermion in the Lipkin model is notably different of those in the other two models. As supplementary problem, the boson-fermion realization and the Lipkin model in the isovector pairing model are investigated.