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

Communications in Theoretical Physics

The Braid Group Representation of IRF Model

Hong-Kang Zhao

Published Dec 1, 1991• 0 citations
Publisher

Abstract

The braid group representations (BGRs) corresponding to IRF model are discussed by solving the spectral-independent Yang-Baxter Equation in the cases and 3. The BGRs obtained here are constant matrices.
DOI
10.1088/0253-6102/16/4/427

Related papers

General Eight–Vertex Model and Braid Group Representation

Mo‐Lin Ge, Hong-Kang Zhao

The braid group representations (BGRs) corresponding to general eight–vertex model are obtained for the case in which the total spins are not conserved. A Yang–Baxterization scheme is applied to obtain from these BGRs.

Communications in Theoretical Physics•Oct 1, 1990•0 citations

GENERAL 8 - VERTEX MODEL AND BRAID GROUP REPRESENTATION

Ml Ge, Hk Zhao, GE, ML (reprint author), NANKAI INST MATH,DIV THEORET PHYS,TIANJIN 300071,PEOPLES R CHINA.

The braid group representations (BGRs) corresponding to general eight-vertex model are obtained for the case in which the total spins are not conserved. A Yang-Baxterization scheme is applied to obtain from these BGRs.

•Jan 1, 1990•0 citations

Yang-Baxterization of the eight-vertex model: the braid group approach

Mo -L Ge, Leh-Hun Gwa, Hong-K Zhao

The braid group representation (BGR) for the eight-vertex model is solved for the case in which the total spins are not conserved. A Yang-Baxterization scheme is applied to obtain from these BGR the spectral-dependent solution; they are found to correspond to the free-fermion and the disorder-point solutions.

Journal of Physics A Mathematical and General•Aug 21, 1990•6 citations

Qubit representations of the braid groups from generalized Yang–Baxter matrices

Jennifer F. Vasquez, Zhenghan Wang, Helen Wong

arXiv:1602.08536•Quantum Information Processing•Apr 15, 2016•4 citations

How to solve Yang–Baxter equation using the Taylor expansion of R-matrix

P. N. Bibikov

arXiv:nlin/0112001•Physics Letters A•Jun 9, 2003•8 citations

Almost local integrable models from supersymmetry algebras

Somnath Maity, Pramod Padmanabhan, Jarmo Hietarinta +1 more

Abstract Supersymmetry algebras can be used to obtain algebraic expressions for constant Yang–Baxter solutions, also known as braid group generators. This was done for non-invertible braid operators in Maity et al (2025 J. High Energy Phys 5 1–31) In this work we extend this construction for the invertible ones. The resulting expressions are then shown to obey relations analogous to those satisfied by quotients of braid groups. Examples of the latter include the Iwahori–Hecke algebra and the Birman–Murakami–Wenzl algebra. As a result, we can Baxterize the constant Yang–Baxter solutions to yield spectral parameter dependent R -matrices. The regularity of these R -matrices depends on the representation of SUSY generators. In some cases they are regular in the usual sense and in the remaining they are ‘almost’ regular. In the latter case they are also non-invertible. Nevertheless, we show that they can still help us construct integrable models in all dimensions of the local Hilbert space. These models can be described by Hamiltonian densities that are either local or non-local, depending on the representation chosen for the SUSY generators. We demonstrate this for all constant 4 × 4 invertible Yang–Baxter solutions. Apart from reproducing nearest-neighbor interaction spin 1 2 systems, we also find their higher spin analogs due to the algebraic [representation independent] approach.

arXiv:2508.04315•Journal of Physics A Mathematical and Theoretical•May 7, 2026•0 citations
Abstract Supersymmetry algebras can be used to obtain algebraic expressions for constant Yang–Baxter solutions, also known as braid group generators. This was done for non-invertible braid operators in Maity et al (2025 J. High Energy Phys 5 1–31) In this work we extend this construction for the invertible ones. The resulting expressions are then shown to obey relations analogous to those satisfied by quotients of braid groups. Examples of the latter include the Iwahori–Hecke algebra and the Birman–Murakami–Wenzl algebra. As a result, we can Baxterize the constant Yang–Baxter solutions to yield spectral parameter dependent R -matrices. The regularity of these R -matrices depends on the representation of SUSY generators. In some cases they are regular in the usual sense and in the remaining they are ‘almost’ regular. In the latter case they are also non-invertible. Nevertheless, we show that they can still help us construct integrable models in all dimensions of the local Hilbert space. These models can be described by Hamiltonian densities that are either local or non-local, depending on the representation chosen for the SUSY generators. We demonstrate this for all constant 4 × 4 invertible Yang–Baxter solutions. Apart from reproducing nearest-neighbor interaction spin 1 2 systems, we also find their higher spin analogs due to the algebraic [representation independent] approach.