Exact solutions of the Cn quantum spin chain

We study the exact solutions of quantum integrable model associated with the C-n Lie algebra, with either a periodic or an open one with off-diagonal boundary reflections, by generalizing the nested off-diagonal Bethe ansatz method. Taking the C-3 as an example we demonstrate how the generalized method works. We give the fusion structures of the model and provide a way to close fusion processes. Based on the resulted operator product identities among fused transfer matrices and some necessary additional constraints such as asymptotic behaviors and relations at some special points, we obtain the eigenvalues of transfer matrices and parameterize them as homogeneous T - Q relations in the periodic case or inhomogeneous ones in the open case. We also give the exact solutions of the C-n model with an off-diagonal open boundary condition. The method and results in this paper can be generalized to other high rank integrable models associated with other Lie algebras. (C) 2021 The Authors. Published by Elsevier B.V.

Automated summary

In this paper, we study the exact solutions of quantum integrable models associated with the C-n Lie algebra by generalizing the Bethe ansatz method. By demonstrating the method with the C-3 model, fusion structures and eigenvalues of transfer matrices are obtained. The results and techniques can be applied to other high rank integrable models associated with different Lie algebras.