Reflection K-Matrices for 19-Vertex Models

Abstract

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.

35 pages, LaTex

Cited by in corpus (33)

• Integrable approach to simple exclusion processes with boundaries. Review and progress
• Boundary quantum group generators of type A
• Classification of reflection matrices related to (super) Yangians and application to open spin chain models
• On $A_{n-1}^{(1)},B_n^{(1)},C_n^{(1)},D_n^{(1)},A_{2n}^{(2)},A_{2n-1}^{(2)}$ and $D_{n+1}^{(2)}$ Reflection $K$-Matrices
• Exact solution of the Izergin-Korepin model with general non-diagonal boundary terms
• Bethe Ansatz solution for quantum spin-1 chains with boundary terms
• Integrability of the $D_n^2$ vertex models with open boundary
• $C_n^{(1)}$, $D_n^{(1)}$ and $A_{2n-1}^{(2)}$ reflection K-matrices
• Exact solution of the one-dimensional super-symmetric t-J model with unparallel boundary fields
• Spectrum of the supersymmetric t-J model with non-diagonal open boundaries
• $A_{n-1}^{(1)}$ Reflection K-Matrices
• Exact solution for the Bariev model with boundary fields
• B_{n}^{(1)} and A_{2n}^{(2)}reflection K-matrices
• D_{n+1}^(2) Reflection K-matrices
• Generalized q-Onsager Algebras and Dynamical K-matrices
• Reflection matrices for the $U_q[sl(m|n{)}^{(1)}]$ vertex model
• Algebraic Bethe Ansatz solutions for the $sl(2|1{)}^{(2)}$ and $osp(2|1)$ models with boundary terms
• Solutions of the reflection equations for the $U_q[G_2]$ vertex model
• New reflection matrices for the U_q(gl(m|n)) case
• On the ${\mathcal{U}}_q[sl(2)]$ Temperley-Lieb reflection matrices
• Quantum group symmetries and completeness for A_{2n}^(2) open spin chains
• Reflection matrices with $U_q[os{p}^{(2)}(2|2m)]$ symmetry
• Integrable open boundary conditions for the Bariev model of three coupled XY spin chains
• Solitons, Boundaries, and Quantum Affine Algebras
• Exact solution of the trigonometric SU(3) spin chain with generic off-diagonal boundary reflections
• Reflection $K$-matrices for a nineteen vertex model with $U_q[\mathrm{osp}{\left(2|2\right)}^{\left(2\right)}]$ symmetry
• A convenient basis for the Izergin-Korepin model
• Algebraic Bethe ansatz for 19-vertex models with upper triangular K-matrices
• $osp(1|2)$ off-shell Bethe ansatz equation with boundary terms
• Reflection equation for the N=3 Cremmer-Gervais R-matrix
• Exact surface energies and boundary excitations of the Izergin-Korepin model with generic boundary fields
• Exact solution of the Izergin-Korepin Gaudin model with periodic and open boundaries
• Refection Matrices for the (n+1)(2n+1)- Vertex Models: Diagonal Solutions