Row Transfer Matrix Functional Relations for Baxter's Eight-Vertex and Six-Vertex Models with Open Boundaries Via More General Reflection Matrices

TL;DR

This paper derives functional relations for transfer matrices of six- and eight-vertex models with open boundaries, using general reflection matrices, and explores their physical properties and interrelations.

Contribution

It introduces more general off-diagonal reflection matrices and establishes the su(2) fusion rule for these boundary conditions.

Findings

Functional relations for transfer matrices are established.

The su(2) fusion rule applies to models with off-diagonal boundary matrices.

Intertwining relations between reflection K matrices are discussed.

Abstract

The functional relations of the transfer matrices of fusion hierachies for six- and eight-vertex models with open boundary conditions have been presented in this paper. We have shown the su($2$) fusion rule for the models with more general reflection boundary conditions, which are represented by off-diagonal reflection matrices. Also we have discussed some physics properties which are determined by the functional relations. Finally the intertwining relation between the reflection $K$ matrices for the vertex and SOS models is discussed.