5 research outputs found
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