Spectrum of the Transfer Matrices of the Spin Chains Associated with the $$A^{(2)}_3$$ A 3 ( 2
Spectrum of the Transfer Matrices of the Spin Chains Associated with the $$A^{(2)}_3$$ A 3 ( 2
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DOI：
10.1007/s00220-022-04566-9
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发表时间：
2022-01
影响因子：
2.4
通讯作者：
Guang-Liang Li;Junpeng Cao;K. Hao;Pei Sun;Xiaotian Xu;Tao Yang;Wen-Li Yang
中科院分区：
文献类型：
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作者：
Guang-Liang Li;Junpeng Cao;K. Hao;Pei Sun;Xiaotian Xu;Tao Yang;Wen-Li Yang
本文研究了与扭曲李代数相关的量子可积系统的精确解，其中边界反射矩阵具有非对角元素，从而使U（1）对称性破缺。借助于融合技术，我们得到了融合后的传递矩阵的封闭递归关系。在此基础上，结合系统的渐近行为和在特殊点处的值，得到了系统的特征值和Bethe渐近方程。我们还证明了该方法对于保留U（1）对称性的周期边界条件是通用的和有效的。本文的结果可用于研究相关的任意可积模型的精确解。
We study the exact solution of quantum integrable system associated with thetwist Lie algebra, where the boundary reflection matrices have non-diagonal elements thus theU(1) symmetry is broken. With the help of the fusion technique, we obtain the closed recursive relations of the fused transfer matrices. Based on them, together with the asymptotic behaviors and the values at special points, we obtain the eigenvalues and Bethe ansatz equations of the system. We also show that the method is universal and valid for the periodic boundary condition where theU(1) symmetry is reserved. The results in this paper can be applied to studying the exact solution of the-related integrable models with arbitraryn.