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arXiv:hep-th/9306089 · Journal of Physics A Mathematical and General

Boundary K-matrices for the XYZ, XXZ and XXX spin chains

Hector J. de Vega, A Gonzalez-Ruiz

Published Sep 21, 1994• 168 citations
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Abstract

The general solutions for the factorization equations of the reflection matrices K +or- ( theta ) for the eight-vertex and six-vertex models (XYZ, XXZ and XXX chains) are found. The associated integrable magnetic Hamiltonians are derived explicitly, finding families depending on several continuous as well as discrete parameters.
DOI
10.1088/0305-4470/27/18/021

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The general solutions for the factorization equations of the reflection matrices Kpm(theta)K^{\\pm}(\\theta)Kpm(theta) for the eight vertex and six vertex models (XYZ, XXZ and XXX chains) are found. The associated integrable magnetic Hamiltonians are explicitly derived, finding families dependig on several continuous as well as discrete parameters.
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The symmetries, especially those related to the R -transformation, of the reflection equation (RE) for two-component systems are analysed. 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 a Baxter type corresponds to the same form of a 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 is obtained with a generalization to the Sklyanin formalism.