论文标题
与$ a^{（2）} _ 3 $ lie代数相关的旋转链的传输矩阵的光谱
Spectrum of the transfer matrices of the spin chains associated with the $A^{(2)}_3$ Lie algebra
论文作者
论文摘要
我们研究了与$ a^{（2）} _ 3 $ twist lie代数相关的量子整合系统的精确解，其中边界反射矩阵具有非二元组元素，因此$ u（1）$对称性被损坏。借助融合技术，我们获得了融合转移矩阵的封闭递归关系。基于它们，以及在特殊点处的渐近行为和值，我们获得了系统的特征值和伯特·安萨兹方程。我们还表明，该方法是通用的，并且对于保留$ u（1）$对称性的周期性边界条件有效。本文中的结果可以应用于研究$ a^{（2）} _ n $相关的具有任意$ n $的集成模型的精确解决方案。
We study the exact solution of quantum integrable system associated with the $A^{(2)}_3$ twist Lie algebra, where the boundary reflection matrices have non-diagonal elements thus the $U(1)$ 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 the $U(1)$ symmetry is reserved. The results in this paper can be applied to studying the exact solution of the $A^{(2)}_n$-related integrable models with arbitrary $n$.
