论文标题
不变子空间和可集成的开放式旋转$ 1/2 $ $ \ xyz $链中的显式bethe向量
Invariant subspaces and explicit Bethe vectors in the integrable open spin $1/2$ $\XYZ$ chain
论文作者
论文摘要
我们得出一个标准，根据该标准，将出现在手学冲击状态下的两个开放$ \ XYZ $ HAMILTONIAN的所有特征状态，分为两个不变子空间。分裂由整数数字支配，该数字具有基础状态最大数量的扭结数的几何含义。我们描述了相应的伯特向量的通用结构。在没有伯特根的情况下，我们获得了贝斯向量的明确表达式，以及一个由一个伯特根生成的表达式，并研究了\倍数。我们还详细描述了一个自旋螺旋状态的椭圆类似物，以周期性和开放的$ \ xyz $模型出现，并得出特征状态。自旋螺旋状态的椭圆类似物的特征是磁化谱的准周期调制，由雅各比椭圆函数控制。
We derive a criterion under which splitting of all eigenstates of an open $\XYZ$ Hamiltonian with boundary fields into two invariant subspaces, spanned by chiral shock states, occurs. The splitting is governed by an integer number, which has the geometrical meaning of the maximal number of kinks in the basis states. We describe the generic structure of the respective Bethe vectors. We obtain explicit expressions for Bethe vectors, in the absence of Bethe roots, and those generated by one Bethe root, and investigate the \multiplet. We also describe in detail an elliptic analogue of the spin-helix state, appearing in both the periodic and the open $\XYZ$ model, and derive the eigenstate condition. The elliptic analogue of the spin-helix state is characterized by a quasi-periodic modulation of the magnetization profile, governed by Jacobi elliptic functions.
