Integrable Vertex Models with General Twists

Details Integrable Vertex Models with General Twists Integrable Vertex Models with General Twists

2005-12-21

arxiv.org/abs/nlin/0512063v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

9 pages, Proceedings of Recent Progress in Solvable Models: RIMS Project, Kyoto, Japan, 20-23 July 2004

Scientific paper

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.

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