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:1412.3383 · Communications in Mathematical Physics

New Elliptic Solutions of the Yang–Baxter Equation

Dmitry Chicherin, Sergey E. Derkachov, Vyacheslav Pavlovich Spiridonov

Published Feb 22, 2016• 14 citations
arXivHTMLPDF
DOI
10.1007/s00220-016-2590-2

Related papers

Embedded elliptic curves and the Yang-Baxter equations

Craig A. Tracy

Physica D Nonlinear Phenomena•Jun 1, 1985•27 citations

New solutions to the Yang-Baxter equation from two-dimensional representations of Uq(sl(2)) at roots of unity

M. Ruiz-Altaba

arXiv:hep-th/9201031•Physics Letters B•Apr 1, 1992•19 citations

The four-state solution of the Yang-Baxter equation

Rinat Kashaev, Vladimir V. Mangazeev

Physics Letters A•Nov 1, 1990•8 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

INTRODUCTION TO THE YANG-BAXTER EQUATION

Michio Jimbo

International Journal of Modern Physics A•Sep 1, 1989•274 citations

New spectral-parameter dependent solutions of the Yang-Baxter equation

Alexander. S. Garkun, Suvendu Barik, Aleksey K. Fedorov +1 more

The Yang-Baxter Equation (YBE) plays a crucial role for studying integrable many-body quantum systems. Many known YBE solutions provide various examples ranging from quantum spin chains to superconducting systems. Models of solvable statistical mechanics and their avatars are also based on YBE. Therefore, new solutions of the YBE could be used to construct new interesting 1D quantum or 2D classical systems with many other far-reaching applications. In this work, we attempt to find (almost) exhaustive set of solutions for the YBE in the lowest dimensions corresponding to a two-qubit case. We develop an algorithm, which can potentially be used for generating new higher-dimensional solutions of the YBE.

arXiv:2401.12710•Jan 23, 2024•3 citations
The Yang-Baxter Equation (YBE) plays a crucial role for studying integrable many-body quantum systems. Many known YBE solutions provide various examples ranging from quantum spin chains to superconducting systems. Models of solvable statistical mechanics and their avatars are also based on YBE. Therefore, new solutions of the YBE could be used to construct new interesting 1D quantum or 2D classical systems with many other far-reaching applications. In this work, we attempt to find (almost) exhaustive set of solutions for the YBE in the lowest dimensions corresponding to a two-qubit case. We develop an algorithm, which can potentially be used for generating new higher-dimensional solutions of the YBE.