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arXiv:nucl-th/0601087

A New Boson Realization of Two-Level Pairing Model in Many-Fermion System and its Classical Counterpart

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

Published Jan 30, 2006• 0 citations
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Abstract

A new method for describing the two-level pairing model in a many-fermion system is presented. Basic idea comes from the Schwinger boson representation for the su(2) cross su(2)-algebra, in which four kinds of boson operators govern the dynamics. It is well known that in the original fermion space, it is almost impossible to introduce any trial state for the variation except the BCS state in the framework of the mean field approximation. However, in the Schwinger boson representation, various trial states can be defined on the condition that the mean field approximation is useful. In these states, the mixed-mode coherent state is mainly discussed in this paper.

DOI
10.48550/arxiv.nucl-th/0601087

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A new method for describing the two-level pairing model in a many-fermion system is presented. Basic idea comes from the Schwinger boson representation for the su(2) cross su(2)-algebra, in which four kinds of boson operators govern the dynamics. It is well known that in the original fermion space, it is almost impossible to introduce any trial state for the variation except the BCS state in the framework of the mean field approximation. However, in the Schwinger boson representation, various trial states can be defined on the condition that the mean field approximation is useful. In these states, the mixed-mode coherent state is mainly discussed in this paper.
A new method for describing the two-level pairing model in a many-fermion system is presented. The basic idea comes from the Schwinger boson representation for the su(2) ⊗ su(2)-algebra, in which four kinds of boson operators govern the dynamics. It is well known that in the original fermion space, it is almost impossible to introduce any trial state for the variation except the BCS state in the framework of the mean field approximation. However, in the Schwinger boson representation, various trial states can be defined on the condition that the mean field approximation is useful. In these states, the su(2) ⊗ su(1,1)-coherent state is mainly discussed in this paper.
Various classical counterparts to the two-level pairing model in a many-fermion system are presented in the Schwinger boson representation. It is shown that one of the key ingredients giving the classical descriptions for quantal systems is the use of various trial states in addition to the su(2) ⊗ su(2)-coherent state, which may be a natural selection for the two-level pairing model governed by the su(2) ⊗ su(2)-algebra. It is pointed out that a spurious behavior such as a sharp phase transition can be avoided by using the other states including the su(2) ⊗ su(1,1)- and su(1,1) ⊗ su(1,1)-coherent states. This contrasts with the situation regarding the usual Hartree-Fock-Bogoliubov and quasi-particle random phase approximations applied to the original fermion system, which yield a sharp phase transition.
Considering the present situation of Lie-algebraic studies of high-temperature superconductivity, a Schwinger-type boson realization of the su(4) algebra is investigated. The basic framework comes from a possible form of the su(n) and the su(n,1) algebras in the Schwinger representation, which was recently proposed by two of the present authors (M. Y. & A. K.), together with J. da Providência. The form investigated in this paper is, in some sense, a natural extension of the Schwinger boson representation for the so(5), so(4) and su(2)⊗su(2) algebras, which was also proposed by the present authors. The orthogonal set for the irreducible representation of the su(4) algebra is completely analogous to that expressed in terms of fermion operators for pairing correlation.