arXiv:2011.02746 · Nuclear Physics B

Exact solutions of the C quantum spin chain

Guang-Liang Li, Panpan Xue, Pei Sun, Hulin Yang, Xiaotian Xu, Junpeng Cao, Tao Yang, Wen‐Li Yang

Published Feb 5, 2021• 5 citations

Abstract

We study the exact solutions of quantum integrable model associated with the Cn 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 C3 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 Cn 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.

DOI: 10.1016/j.nuclphysb.2021.115333

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arXiv:2011.02746 · Nuclear Physics B

Exact solutions of the C quantum spin chain

Guang-Liang Li, Panpan Xue, Pei Sun, Hulin Yang, Xiaotian Xu, Junpeng Cao, Tao Yang, Wen‐Li Yang

Published Feb 5, 2021• 5 citations

arXiv HTML PDF

Abstract

DOI: 10.1016/j.nuclphysb.2021.115333

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Exact solution of the quantum integrable model associated with the twisted

{\mathrm{D}}_3^{(2)}

algebra

Abstract We generalize the nested off-diagonal Bethe ansatz method to study the quantum chain associated with the twisted

{D}_3^{(2)}

D 3 2 algebra (or the

{D}_3^{(2)}

D 3 2 model) with either periodic or integrable open boundary conditions. We obtain the intrinsic operator product identities among the fused transfer matrices and find a way to close the recursive fusion relations, which makes it possible to determinate eigenvalues of transfer matrices with an arbitrary anisotropic parameter η. Based on them, and the asymptotic behaviors and values at certain points, we construct eigenvalues of transfer matrices in terms of homogeneous T − Q relations for the periodic case and inhomogeneous ones for the open case with some off-diagonal boundary reflections. The associated Bethe ansatz equations are also given. The method and results in this paper can be generalized to the

{D}_{n+1}^{(2)}

D n + 1 2 model and other high rank integrable models.

Off-diagonal Bethe Ansatz for the

{D}_3^{(1)}

model

Abstract The exact solutions of the

{D}_3^{(1)}

D 3 1 model (or the so(6) quantum spin chain) with either periodic or general integrable open boundary conditions are obtained by using the off-diagonal Bethe Ansatz. From the fusion, the complete operator product identities are obtained, which are sufficient to enable us to determine spectrum of the system. Eigenvalues of the fused transfer matrices are constructed by the T - Q relations for the periodic case and by the inhomogeneous T- Q one for the non-diagonal boundary reflection case. The present method can be generalized to deal with the

{D}_n^{(1)}

D n 1 model directly.