论文标题
$ C_N $量子旋转链的精确解决方案
Exact solutions of the $C_n$ quantum spin chain
论文作者
论文摘要
我们通过概括嵌套的非基因分子伯特斯ANSATZ方法，研究与$ c_n $ lie代数相关的量子整合模型的确切解决方案。以$ C_3 $为例，我们演示了广义方法的工作原理。我们提供模型的融合结构，并提供了关闭融合过程的方法。基于熔融传输矩阵中的运营商产品标识，以及一些必要的其他约束，例如在某些特殊点上的渐近行为和关系，我们获得了转移矩阵的特征值，并将其作为均质的$ t-q $关系在周期性的情况下或不均匀的情况下以均匀的$ t-q $关系进行参数化。我们还提供了$ C_N $模型的确切解决方案，并具有偏离开放式边界条件。本文中的方法和结果可以推广到与其他Lie代数相关的其他高级积分模型。
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.
