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Progress of Theoretical Physics

A Possible Boson Realization of Generalized Lipkin Model for Many-Fermion System: The su(M + 1)-Algebraic Model in Non-Symmetric Boson Representation

A. Kuriyama, Constança Providência, João da Providência, Y. Tsue, M. Yamamura

Published Jun 1, 2001• 0 citations
Publisher

Abstract

On the basis of the formalism proposed by three of the present authors (A. K., J. P. & M. Y.), the generalized Lipkin model consisting of (M+1) single-particle levels is investigated. This model is essentially a kind of the su(M+1)-algebraic model and, in contrast to the conventional treatment, the case in which fermions are partially occupied in each level is discussed. The scheme for obtaining the orthogonal set for the irreducible representation is presented.

DOI
10.1143/ptp.105.933

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On the basis of the formalism proposed by three of the present authors (A. K., J. P. & M. Y.), the generalized Lipkin model consisting of (M+1) single-particle levels is investigated. This model is essentially a kind of the su(M+1)-algebraic model and, in contrast to the conventional treatment, the case in which fermions are partially occupied in each level is discussed. The scheme for obtaining the orthogonal set for the irreducible representation is presented.
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A new boson representation of the |su(2)su(2)su(2)|-algebra proposed by the present authors for describing the damped and amplified oscillator is examined in the Lipkin model as one of the 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, a third boson is introduced. Through this examination, it is concluded that this representation is very workable for the boson realization of the Lipkin model in any fermion number.
The minimum weight states of the Lipkin model consisting of n single-particle levels and obeying the SU (n) algebra are investigated systematically.The basic idea is to use the SU (2) algebra, which is independent of the SU (n) algebra.This idea has already been presented by the present authors in the case of the conventional Lipkin model consisting of two single-particle levels and obeying the SU (2) algebra.If this idea is followed, the minimum weight states are determined for any fermion number appropriately occupying n single-particle levels.Naturally, the conventional minimum weight state is included: all fermions occupy energetically the lowest single-particle level in the absence of interaction.The cases n = 2, 3, 4, and 5 are discussed in some detail...............