标题： qKZ方程的多项式解和Delta = -1/2时XXZ自旋链的基态 显示英文标题

标题： Polynomial solutions of qKZ equation and ground state of XXZ spin chain at Delta = -1/2

摘要： 积分公式用于与六顶点模型的R矩阵相关的量子Knizhnik-Zamolodchikov方程的多项式解。当变形参数q等于e^{+ - 2 π i/3}且晶格的垂直线数量为奇数时，考虑的解是六顶点模型的非均匀转移矩阵的本征向量。在均匀极限情况下，它是各向异性参数Delta等于-1/2且自旋数目为奇数的反铁磁XXZ自旋链的基态本征向量。获得的该本征向量各分量的积分表示允许证明之前提出的关于其性质的一些猜想。提出了一个新的陈述，将XXZ自旋链的基态分量与Temperley-Lieb环模型联系起来，并进行了证明。 显示英文摘要

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.