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arXiv · 2110.02699

Exact solution of the quantum integrable model associated with the twisted $D^{(2)}_3$ algebra

Guang-Liang Li·Xiaotian Xu·Kun Hao·Pei Sun·Junpeng Cao·Wen-Li Yang·Kangjie Shi·Yupeng Wang
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Abstract

We generalize the nested off-diagonal Bethe ansatz method to study the quantum chain associated with the twisted $D^{(2)}_3$ algebra (or the $D^{(2)}_3$ 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 $\eta$. 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 $D^{(2)}_{n+1}$ model and other high rank integrable models.

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Guang-Liang Li, Xiaotian Xu, Kun Hao, Pei Sun, Junpeng Cao, Wen-Li Yang, Kangjie Shi, Yupeng Wang. 2021-10-06. Exact solution of the quantum integrable model associated with the twisted $D^{(2)}_3$ algebra. https://doi.org/10.1007/jhep03(2022)175

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