The generalisation of the quantum inverse scattering method is used to diagonalise the transfer matrix of Belavin's Z n *Z n symmetric model (1981). The eigenvalues and Bethe ansatz equations are obtained.
We review recent progress towards the solution of exactly solved isotropic vertex models with arbitrary toroidal boundary conditions.Quantum space transformations make it possible the diagonalization of the corresponding transfer matrices by means of the quantum inverse scattering method.Explicit expressions for the eigenvalues and Bethe ansatz equations of the twisted isotropic spin chains based on the Bn,Dn and Cn Lie algebras are presented.The applicability of this approach to the eight vertex model with non-diagonal twists is also discussed.
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.
The Bethe ansatz equations of the 1-D SU(3) Hubbard model are systematically derived by diagonalizing the inhomogeneous transfer matrix of the XXX model. We first derive the scattering matrix of the SU(3) Hubbard model through the coordinate Bethe ansatz method. Then, with the help quantum inverse scattering method we solve the nested transfer matrix and give the eigenvalues, the eigenvectors and the Bethe ansatz equations. Finally, we obtain the exactly analytic solution for the ground state. PACS:05.20.-y; 05.50.+q; 04.20.Jb; 03.65.Fd