Boundary Yang-Baxter equation in the RSOS/SOS representation

Abstract

We construct and solve the boundary Yang-Baxter equation in the RSOS/SOS representation. We find two classes of trigonometric solutions; diagonal and non-diagonal. As a lattice model, these two classes of solutions correspond to RSOS/SOS models with fixed and free boundary spins respectively. Applied to (1+1)-dimenional quantum field theory, these solutions give the boundary scattering amplitudes of the particles. For the diagonal solution, we propose an algebraic Bethe ansatz method to diagonalize the SOS-type transfer matrix with boundary and obtain the Bethe ansatz equations.

30 pages, 5 figures, uses Latex with eepic.sty and epic.sty. Paper substantially expanded; section on SOS model is revised and a new section on the Bethe ansatz equation is added

References in corpus (4)

• Interaction-Round-a-Face Models with Fixed Boundary Conditions: The ABF Fusion Hierarchy
• Row Transfer Matrix Functional Relations for Baxter's Eight-Vertex and Six-Vertex Models with Open Boundaries Via More General Reflection Matrices
• Fusion Hierarchy and Finite-Size Corrections of $U_q[sl(2)]$ Invariant Vertex Models with Open Boundaries
• Integrable O(n) model on the honeycomb lattice via reflection matrices : Surface critical behaviour

Cited by in corpus (25)

• Boundary flows in minimal models
• Boundary Flows in general Coset Theories
• Integrable and Conformal Boundary Conditions for sl(2) A-D-E Lattice Models and Unitary Minimal Conformal Field Theories
• Solutions of the reflection equation for face and vertex models associated with $A_n^{(1)},B_n^{(1)},C_n^{(1)},D_n^{(1)}$ and $A_n^{(2)}$
• 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
• A Construction of Solutions to Reflection Equations for Interaction-Round-a-Face Models
• Integrability of the $D_n^2$ vertex models with open boundary
• Surface Free Energies, Interfacial Tensions and Correlation Lengths of the ABF Models
• Exact boundary S-matrices of the supersymmetric sine-Gordon theory on a half line
• Surface Free Energies and Surface Critical Behaviour of the ABF Models with Fixed Boundaries
• Supersymmetry in the boundary tricritical Ising field theory
• Solutions of the boundary Yang-Baxter equation for ADE models
• An Ising model in a magnetic field with a boundary
• TBA boundary flows in the tricritical Ising field theory
• Complete Nondiagonal Reflection Matrices of RSOS/SOS and Hard Hexagon Models
• Integrable supersymmetric correlated electron chain with open boundaries
• Supersymmetric Sine-Gordon Model and the Eight-Vertex Free Fermion model with Boundary
• Exact solution and surface critical behaviour of open cyclic SOS lattice models
• Solutions of the reflection equations for the $U_q[G_2]$ vertex model
• Spin chains from dynamical quadratic algebras
• Inversion identities for inhomogeneous face models
• Fateev-Zamolodchikov and Kashiwara-Miwa models: boundary star-triangle relations and surface critical properties
• Surface operator content of the A_L face models
• Fusion Hierarchies with Open Boundaries and Exactly Solvable Models
• Boundary reflection matrices of massive ${\varphi }_{1,3}$-perturbed unitary minimal models