Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

理论物理通讯：英文版

BCS Ground State and XXZ Antiferromagnetic Model as SU(2), SU(1,1) Coherent States: An Algebraic Diagonalization Method

Xie, Bing-Hao, Zhang, Hong-Biao, Chen, Jing-Ling

Published Jan 1, 2002• 0 citations
OpenAlex

Abstract

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.

Related papers

BCS Ground State and XXZ Antiferromagnetic Model as SU(2), SU(1,1) Coherent States: An Algebraic Diagonalization Method

Bing-Hao Xie, Hongbiao Zhang, Jing-Ling Chen

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.

Communications in Theoretical Physics•Sep 15, 2002•6 citations

su(1,2) Algebraic Structure of XYZ Antiferromagnetic Model in Linear Spin-Wave Frame

Shuo Jin, Bing-Hao Xie, Zhao-Xian Yu +1 more

The XYZ antiferromagnetic model in linear spin-wave frame is shown explicitly to have an su(1,2) algebraic structure: the Hamiltonian can be written as a linear function of the 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.

Communications in Theoretical Physics•May 1, 2008•2 citations

Algebraic structure and the energy eigenvalue of the Heisenberg antiferromagnetic model

Shuo Jin

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.

Journal of Northeast Normal University•Jan 1, 2006•0 citations

Su(1,2) Algebraic Structure of the XYZ Antiferromagnetic Model in Linear Spin-Wave Frame

Shuo Jin, Bing-Hao Xie, Hongbiao Zhang +1 more

The $XYZ$ antiferromagnetic model in linear spin-wave frame is shown explicitly to have an $su(1,2)$ algebraic structure: the Hamiltonian can be written as a linear function of the $su(1,2)$ 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.

arXiv:cond-mat/0606096•Jun 5, 2006•0 citations

An algebraic diagonalization method to one-dimensional peierls transformation model

Ping Lou

We diagonalized the Hamiltonian of SSH Model with a new algebraic diagonalization method, which could give us the eigenstate at the same time of diagonalization. The result get from this new method was also discussed with the one from the usual Bogoliubov-Valatin transformation method.

Journal of Anhui University•Jan 1, 2005•0 citations

Coherent-state theory of Fermi-Bose superfluid mixture system

Yang Cuixia

To study the coherent states of the Fermi-Bose superfluid mixture system,by using the mean-field approximation and Lie Algebra,it shows that the system is in the SU(2)SU(1,1)coherent-states at T=0.The result of the ground state energy is the same as that of Bogoliubov transformation.However,the coherent state method is convenient than Bogoliubov transformation in treating the BEC-BCS systems because this method can give the both the state function and the corresponding eigenvalues of the systems.

Journal of Fuyang Teachers College•Jan 1, 2010•0 citations
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.
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.
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.
To study the coherent states of the Fermi-Bose superfluid mixture system,by using the mean-field approximation and Lie Algebra,it shows that the system is in the SU(2)SU(1,1)coherent-states at T=0.The result of the ground state energy is the same as that of Bogoliubov transformation.However,the coherent state method is convenient than Bogoliubov transformation in treating the BEC-BCS systems because this method can give the both the state function and the corresponding eigenvalues of the systems.