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

arXiv:2201.00963 · Communications in Mathematical Physics

Spectrum of the Transfer Matrices of the Spin Chains Associated with the $$A^{(2)}_3$$ Lie Algebra

Guang-Liang Li, Junpeng Cao, Kun Hao, Pei Sun, Xiaotian Xu, Tao Yang, Wen‐Li Yang

Published Dec 21, 2022• 1 citation
arXivHTMLPDF
DOI
10.1007/s00220-022-04566-9

Related papers

Exact solution of a quantum integrable system associated with the G2 exceptional Lie algebra

Guang-Liang Li, Junpeng Cao, Pei Sun +3 more

A quantum integrable spin chain model associated with the G 2 exceptional Lie algebra is studied. By using the fusion technique, the closed recursive relations among the fused transfer matrices are obtained. These identities allow us to derive the exact energy spectrum and Bethe ansatz equations of the system based on polynomial analysis. The present method provides a unified treatment to investigate the Bethe ansatz solutions for both the periodic and the non-diagonal open boundary conditions associated with exceptional Lie algebras.

arXiv:2408.04201•Nuclear Physics B•Dec 13, 2024•3 citations

Spectra and Eigenstates of Spin Chain Hamiltonians

Jonathan P. Keating, Noah Linden, H. J. Wells

arXiv:1403.1121•Communications in Mathematical Physics•Apr 30, 2015•81 citations

Analytical Bethe ansatz for a A2n-1(2), Bn(1), Cn(1), Dn(1)quantum-algebra-invariant open spin chains

Simone Artz, Luca Mezincescu, Rafael I. Nepomechie

We determine the eigenvalues of the transfer matrices for integrable open quantum spin chains which are associated with the affine Lie algebras A 2n-1 (2) , B n (1) , C n (1) , D n (1) , and which have the quantum-algebra invariance U q (C n ), U q (B n ), U q (C n ), U q (D n ), respectively.

arXiv:hep-th/9504085•Journal of Physics A Mathematical and General•Sep 21, 1995•42 citations

THE QUANTUM TRANSFER MATRIX AND ITS APPLICATION TO QUANTUM SPIN CHAINS

Kenn Kubo

WORLD SCIENTIFIC eBooks•Dec 1, 1993•1 citation

The spectrum of quantum-group-invariant transfer matrices

Rafael I. Nepomechie, Ana L. Retore

Integrable open quantum spin-chain transfer matrices constructed from trigonometric R-matrices associated to affine Lie algebras g ˆ , and from certain K-matrices (reflection matrices) depending on a discrete parameter p , were recently considered in arXiv:1802.04864 and arXiv:1805.10144 . It was shown there that these transfer matrices have quantum group symmetry corresponding to removing the p th node from the g ˆ Dynkin diagram. Here we determine the spectrum of these transfer matrices by using analytical Bethe ansatz, and we determine the dependence of the corresponding Bethe equations on p . We propose formulas for the Dynkin labels of the Bethe states in terms of the numbers of Bethe roots of each type. We also briefly study how duality transformations are implemented on the Bethe ansatz solutions.

arXiv:1810.09048•Nuclear Physics B•Nov 23, 2018•9 citations

Excitation spectrum of heisenberg spin chains

Vladyslav O. Cheranovskii

Theoretical and Experimental Chemistry•Jan 1, 1988•1 citation
Spectrum of the Transfer Matrices of the Spin Chains Associated with the A3(2)A^{(2)}_3A3(2)​ Lie Algebra
A quantum integrable spin chain model associated with the G 2 exceptional Lie algebra is studied. By using the fusion technique, the closed recursive relations among the fused transfer matrices are obtained. These identities allow us to derive the exact energy spectrum and Bethe ansatz equations of the system based on polynomial analysis. The present method provides a unified treatment to investigate the Bethe ansatz solutions for both the periodic and the non-diagonal open boundary conditions associated with exceptional Lie algebras.
Integrable open quantum spin-chain transfer matrices constructed from trigonometric R-matrices associated to affine Lie algebras g ˆ , and from certain K-matrices (reflection matrices) depending on a discrete parameter p , were recently considered in arXiv:1802.04864 and arXiv:1805.10144 . It was shown there that these transfer matrices have quantum group symmetry corresponding to removing the p th node from the g ˆ Dynkin diagram. Here we determine the spectrum of these transfer matrices by using analytical Bethe ansatz, and we determine the dependence of the corresponding Bethe equations on p . We propose formulas for the Dynkin labels of the Bethe states in terms of the numbers of Bethe roots of each type. We also briefly study how duality transformations are implemented on the Bethe ansatz solutions.