Diagonal solutions to reflection equations in higher spin XXZ model

A general fusion method to find solutions to the reflection equation in higher spin representations starting from the fundamental one is shown. The method is illustrated by applying it to obtaining the $K$ diagonal boundary matrices in an alternating spin $1/2$ and spin $1$ chain. The hamiltonian is also given. The applicability of the method to higher rank algebras is shown by obtaining the $K$ diagonal matrices for a spin chain in the $\left\{ 3^* \right\}$ representation of $su(3)$ from the $\left\{ 3\right\}$ representation.Comment: Plain tex, 10 pages, 4 figures, revised version, some comments are adde

Boundary S-matrix of the O(N)O(N)-symmetric Non-linear Sigma Model

We conjecture that the $O(N)$-symmetric non-linear sigma model in the semi-infinite $(1+1)$-dimensional space is ``integrable'' with respect to the ``free'' and the ``fixed'' boundary conditions. We then derive, for both cases, the boundary S-matrix for the reflection of massive particles of this model off the boundary at $x=0$.Comment: 9 pages, RU-94-0

Quaternion-K\"ahler N=4 Supersymmetric Mechanics

Using the N=4, 1D harmonic superspace approach, we construct a new type of N=4 supersymmetric mechanics involving 4n-dimensional Quaternion-K\"ahler (QK) 1D sigma models as the bosonic core. The basic ingredients of our construction are {\it local} N=4, 1D supersymmetry realized by the appropriate transformations in 1D harmonic superspace, the general N=4, 1D superfield vielbein and a set of 2(n+1) analytic "matter" superfields representing (n+1) off-shell supermultiplets (4, 4, 0). Both superfield and component actions are given for the simplest QK models with the manifolds \mathbb{H}H^n = Sp(1,n)/[Sp(1) x Sp(n)] and \mathbb{H}P^n = Sp(1+n)/[Sp(1) x Sp(n)] as the bosonic targets. For the general case the relevant superfield action and constraints on the (4, 4, 0) "matter" superfields are presented. Further generalizations are briefly discussed.Comment: further minor corrections in eqs. (2.21), (4.24) and (A9

Bethe Ansatz solution for quantum spin-1 chains with boundary terms

The procedure for obtaining integrable open spin chain Hamiltonians via reflection matrices is explicitly carried out for some three-state vertex models. We have considered the 19-vertex models of Zamolodchikov-Fateev and Izergin-Korepin, and the $Z_{2}$-graded 19-vertex models with $sl(2|1)$ and $osp(1|2)$ invariances. In each case the eigenspectrum is determined by application of the coordinate Bethe Ansatz.Comment: 24 pages, LaTex, some misprints remove

Reflection K-Matrices for 19-Vertex Models

We derive and classify all regular solutions of the boundary Yang-Baxter equation for 19-vertex models known as Zamolodchikov-Fateev or $A_{1}^{(1)}$ model, Izergin-Korepin or $A_{2}^{(2)}$ model, sl(2|1) model and osp(2|1) model. We find that there is a general solution for $A_{1}^{(1)}$ and sl(2|1) models. In both models it is a complete K-matrix with three free parameters. For the $A_{2}^{(2)}$ and osp(2|1) models we find three general solutions, being two complete reflection K-matrices solutions and one incomplete reflection K-matrix solution with some null entries. In both models these solutions have two free parameters. Integrable spin-1 Hamiltonians with general boundary interactions are also presented. Several reduced solutions from these general solutions are presented in the appendices.Comment: 35 pages, LaTe