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Acta Physica Sinica

An sus(1,1) ⊕ sud(1,1) algebraic structure of the cuprate superconductors model based on the analogy with atomic nuclei

Shuo Jin, Bing-Hao Xie, Hongbiao Zhang

Published Jan 1, 2012• 0 citations
Publisher

Abstract

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.

DOI
10.7498/aps.61.030304

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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.
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.
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.
We suggest a generic algebraic method to solve non-Hermitian Hamiltonian systems with Lie algebraic linear structure. Such method can not only unify the non-Hermitian Hamiltonian and the Hermitian Hamiltonian with the same structure but also keep self-consistent between similarity transformation and unitary transformation. To clearly reveal the correctness and physical meaning of such algebraic method, we illustrate our method with two different types of non-Hermitian Hamiltonians: the non-Hermitian Hamiltonian with Heisenberg algebraic linear structure and the non-Hermitian Hamiltonian with su(1, 1) algebraic linear structure. We obtain energy eigenvalues and the corresponding eigenstates of non-Hermitian forced harmonic oscillator with Heisenberg algebra structure via a proper similarity transformation. We also calculate the eigen-problems of general non-Hermitian Hamiltonian with su(1, 1) structure in terms of the similarity transformation. As an application, we focus on studying the non-Hermitian single-mode squeezed and coherent harmonic oscillator system and find that such similarity transformation associated with this model is in fact gauge-like transformation for simple harmonic oscillator.