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arXiv:cond-mat/0606097 · Philosophical Magazine Letters

su(3) algebraic structure of the cuprate superconductor model based on the analogy with atomic nuclei

Shuo Jin, B.-H. Xie, H.-B. Zhang, Joseph L. Birman, M. L. Ge

Published Oct 25, 2006• 4 citations
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Abstract

A cuprate superconductor model based on the analogy with atomic nuclei was shown by Iachello to have an su(3) structure. The mean-field approximation Hamiltonian can be written as a linear function of the generators of the su(3) algebra. Using algebraic methods, we derive the eigenvalues of the reduced Hamiltonian beyond the subalgebras u(1)⊗ u(2) and so(3) of the su(3) algebra. In particular, by considering the coherence between s- and d-wave pairs as a perturbation, the effects of the coherent term upon the energy spectrum are investigated.

DOI
10.1080/09500830600993303

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A cuprate superconductor model based on the analogy with atomic nuclei was shown by Iachello to have an su(3) structure. The mean-field approximation Hamiltonian can be written as a linear function of the generators of the su(3) algebra. Using algebraic methods, we derive the eigenvalues of the reduced Hamiltonian beyond the subalgebras u(1)⊗ u(2) and so(3) of the su(3) algebra. In particular, by considering the coherence between s- and d-wave pairs as a perturbation, the effects of the coherent term upon the energy spectrum are investigated.
A cuprate superconductor model based on the analogy with atomic nuclei was presented to have an su(3) algebraic structure by Iachello. Our previous work showed that the mean-field approximation Hamiltonian can be expressed as a linear function of the generator of su(3) algebra. Through the realization of the algebra generator, an sus(1,1) ⊕ sud(1,1) algebraic structure is shown. By using the unitary transformation of the coherent operator U(θ,φ), the gap equations and the eigenvalues of the reduced Hamiltonian are obtained. The analysis of the physical model through different algebraic structures leads to different particular results.
A U(3) model proposed by Iachello for superconductivity in cuprate materials is analyzed. The model consists of s and d pairs (approximated as bosons) in a two-dimensional Fermi system with a surface. The transition occurs between a phase in which the system is a condensate of one type of boson, and a phase which is a mixture of two types of bosons. In the current work we have investigated the validity of the Bogoliubov approximation, and we used a reduced Hamiltonian to determine a phase diagram, the symmetry of the phases, and the temperature dependence of the heat capacity.
The XYZXYZXYZ antiferromagnetic model in linear spin-wave frame is shown explicitly to have an su(1,2)su(1,2)su(1,2) algebraic structure: the Hamiltonian can be written as a linear function of the su(1,2)su(1,2)su(1,2) algebra generators. Based on it, the energy eigenvalues are obtained by making use of the similar transformations, and the algebraic diagonalization method is investigated. Some numerical solutions are given, and the results indicate that only one group solution could be accepted in physics.
An algebraic diagonalization method is proposed. As two examples, the Hamiltonians of BCS ground stateunder mean-field approximation and XXZ antiferromagnetic model in linear spin-wave frame have been diagonalized byusing SU(2), SU(1,1) Lie algebraic method, respectively. Meanwhile, the eigenstates of the above two models are revealedto be SU(2), SU(1,1) coherent states, respectively. The relation between the usual Bogoliubov Valatin transformationand the algebraic method in a special case is also discussed.