Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-08-14
J.Phys.A32:3505-3523,1999
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX, 16 pages
Scientific paper
10.1088/0305-4470/32/19/304
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.
Ju Guo-xing
Liu Cong-xin
Wang Shi-Kun
Wu Ke
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