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 transfer matrices satisfy a group of functional relations, which are 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 Uq[sl(2)]. In the case of the parameter qh = −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 the 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 underlying conformal field theory are extracted. To see different boundary conditions we also have studied the six-vertex model with a twisted boundary condition. hep-th/9502053; to appear in NPB. 1
A bstract In this paper, we investigate the spectral properties of the staggered six-vertex model with
Z2 Z 2 symmetry for arbitrary system sizes L using non-linear integral equations (NLIEs). Our study is motivated by two key questions: what is the accuracy of results based on the ODE/IQFT correspondence in the asymptotic regime of large system sizes, and what is the optimal approach based on NLIE for analyzing the staggered six-vertex model? We demonstrate that the quantization conditions for low-lying primary and descendant states, derived from the ODE/IQFT approach in the scaling limit, are impressively accurate even for relatively small system sizes. Specifically, in the anisotropy parameter range π /4 < γ < π /2, the difference between NLIE and ODE/IQFT results for energy and quasi-momentum eigenvalues is of order
O(L−2) O L − 2 . Furthermore, we present a unifying framework for NLIEs, distinguishing between versions with singular and regular kernels. We provide a compact derivation of NLIE with a singular kernel, followed by an equivalent set with a regular kernel. We address the stability issues in numerical treatments and offer solutions to achieve high-accuracy results, validating our approach for system sizes ranging from L = 2 to L = 10 24 . Our findings not only validate the ODE/IQFT approach for finite system sizes but also enhance the understanding of NLIEs in the context of the staggered six-vertex model. We hope the insights gained from this study have significant implications for resolving the spectral problem of other lattice systems with emergent non-compact degrees of freedom and provide a foundation for future research in this domain.