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:solv-int/9712011 · International Journal of Modern Physics A

BOUNDARY K MATRICES AND THE LAX PAIR FOR ONE-DIMENSIONAL OPEN XYZ SPIN-CHAIN

Ju Guo-Xing, Shikun Wang, Ke Wu, Chi Xiong

Published Sep 30, 1998• 5 citations
arXivHTMLPDF

Abstract

We analyze the symmetries of the reflection equation for open XYZ model and find their solutions K± case by case. In the general open boundary conditions, the Lax pair for open one-dimensional XYZ spin-chain is given.
DOI
10.1142/s0217751x98002006

Related papers

THE LAX PAIR AND ITS BOUNDARY K MATRIX-FOR XYZ SPIN OPEN CHAIN

GUAN XI-WEN, Tong Dian-Min, Huan-Qiang Zhou +1 more

The Lax pair for the XYZ model under the open boundary condition is explicitly constructed and the general boundary K matrices are obtained.

Acta Physica Sinica•Jan 1, 1997•0 citations

Lax pair formulation for the open boundary Osp(1∣2) spin chain

Xiaoyu Zhang, Kun Hao

Abstract Based on the Lax pair formulation, we study the integrable conditions of the Osp(1∣2) spin chain with open boundaries. We consider both the non-graded and graded versions of the Osp(1∣2) chain. The Lax pair operators M ± for the boundaries can be induced by the Lax operator M j for the bulk of the system. They correspond to the reflection equations (RE) and the Yang–Baxter equation, respectively. We further calculate the boundary K-matrices for both the non-graded and graded versions of the model with open boundaries. The double row monodromy matrix and transfer matrix of the spin chain have also been constructed. The K-matrices obtained from the Lax pair formulation are consistent with those from Sklyanin’s RE. This construction is another way to prove the quantum integrability of the Osp(1∣2) chain. We find that the Lax pair formulation has advantages in dealing with the boundary terms of the supersymmetric model.

Communications in Theoretical Physics•Sep 1, 2022•0 citations

On the Integrability of the One-Dimensional Open XYZ Spin Chain

Ju Guo-Xing, Xiong Chi

The Lax pair for the one-dimensional open XYZ spin chain is constructed, this shows that the system is completely integrable.

arXiv:solv-int/9711004•Communications in Theoretical Physics•Oct 30, 1998•0 citations

LAX PAIR FORMULATION FOR ONE-DIMENSIONAL-LATTICE SPIN OPEN CHAINS

Huan-Qiang Zhou, 重庆大学应用物理系

The Lax pair formulation is presented for quantum completely integrable lattice spin open chains.Specifically,the Lax pair for the one-dimensional Heisenberg XXZ open chain with the general boundary terms is explicitly constructed.The construction provides an alternative and direct demonstration for the quantum integrability of the system.

Acta Physica Sinica•Jan 1, 1997•0 citations

General boundary conditions for the and open spin chains

D. Arnaudon, Jean Avan, Nicolas Crampé +3 more

Two types of boundary conditions (‘soliton preserving’ and ‘soliton non-preserving’) are investigated for the and open spin chains. The appropriate reflection equations are formulated and the corresponding solutions are classified. The symmetry and the Bethe ansatz equations are derived for each case. The general treatment for non-diagonal reflection matrices associated with the ‘soliton preserving’ case is worked out. The connection between the ‘soliton non-preserving’ boundary conditions and the twisted (super-) Yangians is also discussed.

arXiv:math-ph/0406021•Journal of Statistical Mechanics Theory and Experiment•Aug 24, 2004•79 citations

Lax Pair Formulation for the One-Dimensional Heisenberg XYZ Open Chain

Xi‐Wen Guan, D. M. Tong, Huan-Qiang Zhou

The Lax pair for the one-dimensional Heisenberg XYZ open chain is explicitly constructed. Our construction provides an alternative and direct demonstration for the quantum integrability of the system.

Journal of the Physical Society of Japan•Sep 15, 1996•6 citations
Abstract Based on the Lax pair formulation, we study the integrable conditions of the Osp(1∣2) spin chain with open boundaries. We consider both the non-graded and graded versions of the Osp(1∣2) chain. The Lax pair operators M ± for the boundaries can be induced by the Lax operator M j for the bulk of the system. They correspond to the reflection equations (RE) and the Yang–Baxter equation, respectively. We further calculate the boundary K-matrices for both the non-graded and graded versions of the model with open boundaries. The double row monodromy matrix and transfer matrix of the spin chain have also been constructed. The K-matrices obtained from the Lax pair formulation are consistent with those from Sklyanin’s RE. This construction is another way to prove the quantum integrability of the Osp(1∣2) chain. We find that the Lax pair formulation has advantages in dealing with the boundary terms of the supersymmetric model.
Two types of boundary conditions (‘soliton preserving’ and ‘soliton non-preserving’) are investigated for the and open spin chains. The appropriate reflection equations are formulated and the corresponding solutions are classified. The symmetry and the Bethe ansatz equations are derived for each case. The general treatment for non-diagonal reflection matrices associated with the ‘soliton preserving’ case is worked out. The connection between the ‘soliton non-preserving’ boundary conditions and the twisted (super-) Yangians is also discussed.