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:math-ph/0510078 · Nuclear Physics B

On baxterized solutions of reflection equation and integrable chain models

Alexey P. Isaev, O. Ogievetsky

Published Oct 11, 2006• 37 citations
arXivHTMLPDF
DOI
10.1016/j.nuclphysb.2006.09.013

Related papers

Yang-Baxter equation and reflection equations in integrable models

P. P. Kulish

arXiv:hep-th/9507070•Lecture notes in physics•Jan 1, 1996•20 citations

Reflection K-Matrices of the 19-Vertex Model and XXZ Spin-1 Chain with General Boundary Terms

Takeo Inami, Satoru Odake, Yao-Zhong Zhang

We derive and classify all solutions of the boundary Yang-Baxter equation (or the reflection equation) for the 19-vertex model associated with U_q(\\widehat{sl_2}). Integrable XXZ spin-1 chain hamiltonian with general boundary interactions is also obtained.

•Jan 1, 1996•27 citations

Integrable high-spin chain related to the elliptic solution of the Yang-Baxter equation

Rui‐Hong Yue

We discuss the higher-dimensional solutions of the Yang-Baxter equation and reflection equation in the elliptic case. The Hamiltonian of a spin-1 quantum anisotropic chain with non-trivial boundary term is given.

Journal of Physics A Mathematical and General•Mar 7, 1994•7 citations

Aspects of Integrable Models

Costas John Efthimiou

•Jan 1, 1994•0 citations

Integrable Matrix Product States from boundary integrability

Balázs Pozsgay, Lorenzo Piroli, Eric Vernier

We consider integrable Matrix Product States (MPS) in integrable spin chains and show that they correspond to “operator valued” solutions of the so-called twisted Boundary Yang-Baxter (or reflection) equation. We argue that the integrability condition is equivalent to a new linear intertwiner relation, which we call the “square root relation”, because it involves half of the steps of the reflection equation. It is then shown that the square root relation leads to the full Boundary Yang-Baxter equations. We provide explicit solutions in a number of cases characterized by special symmetries. These correspond to the “symmetric pairs” (SU(N),SO(N)) and (SO(N),SO(D) \otimes ⊗ SO(N-D)), where in each pair the first and second elements are the symmetry groups of the spin chain and the integrable state, respectively. These solutions can be considered as explicit representations of the corresponding twisted Yangians, that are new in a number of cases. Examples include certain concrete MPS relevant for the computation of one-point functions in defect AdS/CFT.

arXiv:1812.11094•SciPost Physics•May 27, 2019•49 citations

Integrable Chain Models With Staggered R-Matrices

A. Sedrakyan

arXiv:cond-mat/0112077•Springer eBooks•Jan 1, 2002•6 citations
We consider integrable Matrix Product States (MPS) in integrable spin chains and show that they correspond to “operator valued” solutions of the so-called twisted Boundary Yang-Baxter (or reflection) equation. We argue that the integrability condition is equivalent to a new linear intertwiner relation, which we call the “square root relation”, because it involves half of the steps of the reflection equation. It is then shown that the square root relation leads to the full Boundary Yang-Baxter equations. We provide explicit solutions in a number of cases characterized by special symmetries. These correspond to the “symmetric pairs” (SU(N),SO(N)) and (SO(N),SO(D) \otimes ⊗ SO(N-D)), where in each pair the first and second elements are the symmetry groups of the spin chain and the integrable state, respectively. These solutions can be considered as explicit representations of the corresponding twisted Yangians, that are new in a number of cases. Examples include certain concrete MPS relevant for the computation of one-point functions in defect AdS/CFT.