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

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

Addendum to ``Integrability of Open Spin Chains with Quantum Algebra Symmetry''

We show that the quantum-algebra-invariant open spin chains associated with the affine Lie algebras $A^{(1)}_n$ for $n>1$ are integrable. The argument, which applies to a large class of other quantum-algebra-invariant chains, does not require that the corresponding $R$ matrix have crossing symmetry.Comment: 4 pages, plain tex, UMTG-16

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

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

Fusion Hierarchy and Finite-Size Corrections of Uq[sl(2)]U_q[sl(2)] Invariant Vertex Models with Open Boundaries

The fused six-vertex models with open boundary conditions are studied. The Bethe ansatz solution given by Sklyanin has been generalized to the transfer matrices of the fused models. We have shown that the eigenvalues of transfer matrices satisfy a group of functional relations, which are the $su$(2) fusion rule held by the transfer matrices of the fused models. The fused transfer matrices form a commuting family and also commute with the quantum group $U_q[sl(2)]$. In the case of the parameter $q^h=-1$ ($h=4,5,\cdots$) the functional relations in the limit of spectral parameter u\to \i\infty are truncated. This shows that the $su$(2) fusion rule with finite level appears for the six vertex model with the open boundary conditions. We have solved the functional relations to obtain the finite-size corrections of the fused transfer matrices for low-lying excitations. From the corrections the central charges and conformal weights of underlying conformal field theory are extracted. To see different boundary conditions we also have studied the six-vertex model with a twisted boundary condition.Comment: Pages 29; revised versio