Classification of Solutions to Reflection Equation of Two-Component Systems

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.

LaTeX, 16 pages

References in corpus (2)

• Boundary K-matrices and the Lax pair for 1D open XYZ spin-chain
• Classification of seven-vertex solutions of the coloured Yang-Baxter equation

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