On the algebraic Bethe ansatz: Periodic boundary conditions

In this paper, the algebraic Bethe ansatz with periodic boundary conditions is used to investigate trigonometric vertex models associated with the fundamental representations of the non-exceptional Lie algebras. This formulation allow us to present explicit expressions for the eigenvectors and eigenvalues of the respective transfer matrices.Comment: 36 pages, LaTex, Minor Revisio

Quantum spin chain with "soliton non-preserving" boundary conditions

We consider the case of an integrable quantum spin chain with "soliton non-peserving" boundary conditions. This is the first time that such boundary conditions have been considered in the spin chain framework. We construct the transfer matrix of the model, we study its symmetry and we find explicit expressions for its eigenvalues. Moreover, we derive a new set of Bethe ansatz equations by means of the analytical Bethe ansatz method.Comment: 12 pages, LaTeX, two appendices added, minor correction

Multi-Colour Braid-Monoid Algebras

We define multi-colour generalizations of braid-monoid algebras and present explicit matrix representations which are related to two-dimensional exactly solvable lattice models of statistical mechanics. In particular, we show that the two-colour braid-monoid algebra describes the Yang-Baxter algebra of the critical dilute A-D-E models which were recently introduced by Warnaar, Nienhuis, and Seaton as well as by Roche. These and other solvable models related to dense and dilute loop models are discussed in detail and it is shown that the solvability is a direct consequence of the algebraic structure. It is conjectured that the Yang-Baxterization of general multi-colour braid-monoid algebras will lead to the construction of further solvable lattice models.Comment: 32 page