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Classification of Solutions to Reflection Equation of Two-Component Systems

Cong-xin Liu·Guo-xing Ju·Shi-kun Wang·Ke Wu
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Abstract

The symmetries, especially those related to the $R$-transformation, of the reflection equation(RE) for two-component systems are analyzed. The classification of solutions to the RE for eight-, six- and seven-vertex type $R$-matrices is given. All solutions can be obtained from those corresponding to the standard $R$-matrices by $K$-transformation. For the free-Fermion models, the boundary matrices have property $tr K_+(0)=0$, and the free-Fermion type $R$-matrix with the same symmetry as that of Baxter type corresponds to the same form of $K_-$-matrix for the Baxter type. We present the Hamiltonians for the open spin systems connected with our solutions. In particular, the boundary Hamiltonian of seven-vertex models was obtained with a generalization to the Sklyanin's formalism.

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Cong-xin Liu, Guo-xing Ju, Shi-kun Wang, Ke Wu. 1998-08-14. Classification of Solutions to Reflection Equation of Two-Component Systems. https://doi.org/10.1088/0305-4470%2F32%2F19%2F304

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