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Journal of Physics A Mathematical and General

Generalized Bethe ansatz with the general spin representations of the Sklyanin algebra

Takashi Takebe

Published Mar 7, 1992• 24 citations
Publisher

Abstract

The quantum inverse scattering method is applied to the inhomogeneous Heisenberg XYZ model with general spins, i.e. the general spin representations of the Sklyanin algebra. By means of the generalized Bethe ansatz developed by Takhtajan and Faddeev (1979) the eigenvectors and eigenvalues of the transfer matrix are found.
DOI
10.1088/0305-4470/25/5/015

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Generalized XYZXYZXYZ Model Associated to Sklyanin Algebra∗^*∗
The free energy of a lattice model, which is a generalization of the Heisenberg XYZXYZXYZ model with the higher spin representation of the Sklyanin algebra, is calculated by the generalized Bethe Ansatz of Takhtajan and Faddeev. (Talk given at the XXI Differential Geometry Methods in Theoretical Physics, Tianjin, China 5-9 June 1992)
A generalization of the eight-vertex model by means of higher spin representations of the Sklyanin algebra is investigated by the quantum inverse scattering method and the algebraic Bethe ansatz. Under the well known string hypothesis low-lying excited states are considered and scattering phase shifts of two physical particles are calculated. The S-matrix of two-particle states is shown to be proportional to Baxter`s (1972) elliptic R-matrix with a different elliptic modulus from the original one.
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