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Journal of Physics A Mathematical and General

A new multi-fermion realization of (2) and its application to the Lipkin - Meshkov - Glick model

Fuli Li, Shengli Zhang, Qing Huang

Published Aug 7, 1996• 1 citation
Publisher

Abstract

A new multi-fermion realization of is built, whose generators have been written as functions of operators of su(2) algebra. With the help of the realization, the influence of the q-deformation of su(2) algebra on the excitation spectrum and the ground state properties of the Lipkin - Meshkov - Glick model can easily be understood. It is also shown that the variation approach on the basis of the usual su(2) coherent state still works well for the q-deformed model.

DOI
10.1088/0305-4470/29/15/029

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A new multi-fermion realization of is built, whose generators have been written as functions of operators of su(2) algebra. With the help of the realization, the influence of the q-deformation of su(2) algebra on the excitation spectrum and the ground state properties of the Lipkin - Meshkov - Glick model can easily be understood. It is also shown that the variation approach on the basis of the usual su(2) coherent state still works well for the q-deformed model.
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. The 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 simple form. 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 from that in the other two models. As the supplementary problem, the boson-fermion realization and the Lipkin model in the isovector pairing model are investigated.