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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 PhysicsOct 1, 19900 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, 19900 citations

The Braid Group Representation of IRF Model

Hong-Kang Zhao

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.

Communications in Theoretical PhysicsDec 1, 19910 citations

Yang-Baxterization of Spin-1 L Operator

Mo‐Lin Ge, Xu‐Feng Liu

The Yang-Baxterization of L operator is performed for spin-1 model, namely, for given braid group representation (BGR) the x -dependent L ( x ) operator can be determined where x is the spectral parameter. It is pointed out that in order to establish such an x -dependence besides the usual L ± operators in accordance with the Faddeev-Reshetikhin-Takhtajan (FRT) approach an additional operator L 0 should be introduced. The explicit expression of L 0 is given. This Yang-Baxterization prescription preserves the FRT and the YBE is satisfied by L ( x ) and R ( x ).The Yang-Baxterization of L operator is performed for spin-1 model, namely, for given braid group representation (BGR) the x -dependent L ( x ) operator can be determined where x is the spectral parameter. It is pointed out that in order to establish such an x -dependence besides the usual L ± operators in accordance with the Faddeev-Reshetikhin-Takhtajan (FRT) approach an additional operator L 0 should be introduced. The explicit expression of L 0 is given. This Yang-Baxterization prescription preserves the FRT and the YBE is satisfied by L ( x ) and R ( x ).

Communications in Theoretical PhysicsJul 1, 19921 citation

PARAMETRIZED EIGHT-VERTEX MODEL AND KNOT INVARIANT

T.K. Kassenova

The article discusses and expands the known elements of the eight-vertex model, paying special attention to the parameterization of the matrix. The matrix values are interconnected with the knot through the braids and this model is valid on finite square lattices in two-dimensional space. A new solution of the parametrized eight-vertex model of free fermions with a complex version of elliptic functions, which is valid on a finite lattice, will be constructed. The range of applicability of the eight-vertex model with elements of the Jacobi elliptic function and the construction of a knot invariant on its basis is discussed by comparing the results obtained analytically for the model. The construction of the knot invariant using the Clebsch-Gordan coefficients and the main tool of statistical mechanics of the Yang-Baxter equation will be studied in detailThe article discusses and expands the known elements of the eight-vertex model, paying special attention to the parameterization of the matrix. The matrix values are interconnected with the knot through the braids and this model is valid on finite square lattices in two-dimensional space. A new solution of the parametrized eight-vertex model of free fermions with a complex version of elliptic functions, which is valid on a finite lattice, will be constructed. The range of applicability of the eight-vertex model with elements of the Jacobi elliptic function and the construction of a knot invariant on its basis is discussed by comparing the results obtained analytically for the model. The construction of the knot invariant using the Clebsch-Gordan coefficients and the main tool of statistical mechanics of the Yang-Baxter equation will be studied in detail

Eurasian Physical Technical JournalMar 28, 20221 citation

Solutions of Yang–Baxter equation in the vertex model and the face model for octet representation

Bo-Yu Hou, Bo-Yuan Hou, Zhong-Qi Ma +1 more

In this paper, the solutions of the Yang–Baxter equation both in the vertex model (R matrix) and in the face model (braiding matrix) are computed explicitly for the octet representation of the quantum Kac–Moody A(1)2 enveloping algebra where there is multiplicity greater than one in the decomposition of the coproduct 8⊗8.

Journal of Mathematical PhysicsAug 1, 19913 citations

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

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

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