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 $B_n$ , $D_n$ and $C_n$ Lie algebras are presented. The applicability of this approach to the eight vertex model with non-diagonal twists is also discussed.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 $B_n$, $D_n$ and $C_n$ Lie algebras are presented. The applicability of this approach to the eight vertex model with non-diagonal twists is also discussed.

arXiv:nlin/0512063Dec 21, 20050 citations

B_n

D_n

and

C_n

Lie algebras are presented. The applicability of this approach to the eight vertex model with non-diagonal twists is also discussed.