Exact solution of the B1 model

Abstract

The B1 vertex model is studied by the off-diagonal Bethe ansatz method. New closed operator product identities of the fused transfer matrices are obtained by using the fusion technique. Based on them and the asymptotic behaviors as well as the values of the fused transfer matrices at certain points, the exact solutions of the B1 model with periodic and with integrable off-diagonal open boundary conditions are obtained. We find that the degree of the polynomial of the inhomogeneous T − Q relation is lower. The B1 model is equivalent to the integrable spin-1 Heisenberg chain, thus the method and the results in this paper can be generalized to the high spin Heisenberg model and the integrable models associated with Bn Lie algebra.