Algebraic Bethe ansatz for eight vertex model with general open-boundary conditions

Abstract

By using the intertwiner and face-vertex correpondence relation, we obtain the Bethe ansatz equation of eight vertex model with open boundary condtitions in the framework of algebraic Bethe ansatz method. The open boundary condition under consideration is the general solution of the reflection equation for eight vertex model with only one restriction on the free parameters of the right side reflecting boundary matrix. The reflecting boundary matrices used in this paper thus may have off-diagonal elements. Our construction can also be used for the Bethe ansatz of SOS model with reflection boundaries.

Latex document, several figures, 85KB

References in corpus (17)

• Boundary S-Matrix and Boundary State in Two-Dimensional Integrable Quantum Field Theory
• Boundary K-Matrices for the Six Vertex and the n(2n-1) A_{n-1} Vertex Models
• Exact solution of a massless scalar field with a relevant boundary interaction
• Boundary K-matrices for the XYZ, XXZ AND XXX spin chains
• XXZ chain with a boundary
• Analytical Bethe Ansatz for Quantum-Algebra-Invariant Spin Chains
• Integrable XYZ Spin Chain with Boundaries
• Difference Equations in Spin Chains with a Boundary
• Deriving Boundary S Matrices
• Exact solution of the $S{U}_q(n)$ invariant quantum spin chains
• Integrable vertex and loop models on the square lattice with open boundaries via reflection matrices
• Row Transfer Matrix Functional Relations for Baxter's Eight-Vertex and Six-Vertex Models with Open Boundaries Via More General Reflection Matrices
• Exact Bethe Ansatz solution for $A_{n-1}$ chains with non-$S{U}_q(n)$ invariant open boundary conditions
• Supersymmetric extension of the sine-Gordon theory with integrable boundary interactions
• Bethe Ansatz and Quantum Groups: The Light--Cone Approach. II. From RSOS($p+1$) models to $p-$restricted Sine--Gordon Field Theories
• Exact diagonalization of the quantum supersymmetric $S{U}_q(n|m)$ model
• Fusion Hierarchy and Finite-Size Corrections of $U_q[sl(2)]$ Invariant Vertex Models with Open Boundaries

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