No abstract

In this work we consider a functional method in the theory of exactly solvable models based on the Yang-Baxter algebra. Using this method we derive the eigenvalues of the XXZ model with non-diagonal twisted and open boundary conditions for general values of the anisotropy and boundary parameters.

In this work we refine the method of [1] and obtain a novel kind of functional equation determining the partition function of the elliptic SOS model with domain wall boundaries. This functional relation is originated from the dynamical Yang-Baxter algebra and its solution is given in terms of multiple contour integrals.Comment: v2: details of derivations and reference added, typos fixed, accepted for publication in NP

The integrable structure of the one-dimensional Hubbard model is based on Shastry's R-matrix and the Yangian of a centrally extended sl(2|2) superalgebra. Alcaraz and Bariev have shown that the model admits an integrable deformation whose R-matrix has recently been found. This R-matrix is of trigonometric type and here we derive its underlying exceptional quantum affine algebra. We also show how the algebra reduces to the above-mentioned Yangian and to the conventional quantum affine sl(2|2) algebra in two special limits.

In this paper we investigate trigonometric vertex models associated with solutions of the Yang-Baxter equation which are invariant relative to q-deformed superalgebras sl(r|2m) (2) , osp(r|2m) (1) and osp(r = 2n|2m) (2) . The associated R-matrices are presented in terms of the standard Weyl basis making possible the formulation of the quantum inverse scattering method for these lattice models. This allowed us to derive the eigenvectors and the eigenvalues of the corresponding transfer matrices as well as explicit expressions for the Bethe ansatz equations.