Fusion hierarchy and finite-size corrections of Uq[ sl(2)]-invariant vertex models with open boundaries

Abstract

The fused six-vertex models with open boundary conditions are studied. The Bethe ansatz solution given by Sklyanin has been generalized to the transfer matrices of the fused models. We have shown that the eigenvalues of the transfer matrices satisfy a group of functional relations, which is the su(2) fusion rule held by the transfer matrices of the fused models. The fused transfer matrices form a commuting family and also commute with the quantum group U q [ sl(2)]. In the case of the parameter q h = −1 ( h = 4, 5, …) the functional relations in the limit of spectral parameter u → i∞ are truncated. This shows that the su(2) fusion rule with finite level appears for the six-vertex model with open boundary conditions. We have solved the functional relations to obtain the finite-size corrections of the fused transfer matrices for low-lying excitations. From the corrections the central charges and conformal weights of the underlying conformal field theory are extracted. To see the effect of different boundary conditions we also have studied the six-vertex model with a twisted boundary condition.