qKZ方程的多项式解和XXZ自旋链在Delta = -1/2处的基态
Polynomial solutions of qKZ equation and ground state of XXZ spin chain at Delta = -1/2
摘要：
考虑了与六顶点模型的R-矩阵相关的量子Knizhnik-Zamolodchikov方程的多项式解的积分公式。证明了当变形参数q = e^{+-2 π i/3}，格子的垂线数为奇数时，所考虑的解是六顶点模型的非齐次传递矩阵的一个特征向量。在均匀极限下，它是反铁磁XXZ自旋链的基态本征矢量，各向异性参数δ =-1/2，有奇数个反铁磁自旋链。所获得的积分表示的本征向量的组件允许证明其性质制定较早的一些programmures。本文提出并证明了XXZ自旋链的基态分量与Temperley-Lieb环模型之间的关系。
英文摘要：
Integral formulae for polynomial solutions of the quantum Knizhnik-Zamolodchikov equations associated with the R-matrix of the six-vertex model are considered. It is proved that when the deformation parameter q is equal to e^{+- 2 pi i/3} and the number of vertical lines of the lattice is odd, the solution under consideration is an eigenvector of the inhomogeneous transfer matrix of the six-vertex model. In the homogeneous limit it is a ground state eigenvector of the antiferromagnetic XXZ spin chain with the anisotropy parameter Delta equal to -1/2 and odd number of sites. The obtained integral representations for the components of this eigenvector allow to prove some conjectures on its properties formulated earlier. A new statement relating the ground state components of XXZ spin chains and Temperley-Lieb loop models is formulated and proved.
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