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Journal of Northeast Normal University

Algebraic structure and the energy eigenvalue of the Heisenberg antiferromagnetic model

Shuo Jin

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

Under the linear spin-wave frame,the XYZ antiferromagnetic model is proposed to have su(1,2) algebraic structure.By making use of the algebraic diagonalization method,the energy eigenvalue solutions are obtained through the similar transformation.These offer more foundations for the theoretical analysis of this model in physics and for the applications of algebraic diagonalization method in physical models.

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Communications in Theoretical Physics•Sep 15, 2002•6 citations
Under the linear spin-wave frame,the XYZ antiferromagnetic model is proposed to have su(1,2) algebraic structure.By making use of the algebraic diagonalization method,the energy eigenvalue solutions are obtained through the similar transformation.These offer more foundations for the theoretical analysis of this model in physics and for the applications of algebraic diagonalization method in physical models.
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 state under mean-field approximation and XXZ antiferromagnetic model in linear spin-wave frame have been diagonalized by using SU(2), SU(1,1) Lie algebraic method, respectively. Meanwhile, the eigenstates of the above two models are revealed to be SU(2), SU(1,1) coherent states, respectively. The relation between the usual Bogoliubov–Valatin transformation and the algebraic method in a special case is also discussed.