论文标题
开放的XXZ链为$δ= -1/2 $和边界量子knizhnik-Zamolodchikov方程
The open XXZ chain at $Δ=-1/2$ and the boundary quantum Knizhnik-Zamolodchikov equations
论文作者
论文摘要
使用各向异性参数$δ= - \ frac12 $和依赖于参数$ x $的对角线边界磁场的开放XXZ自旋链。对于真正的$ x> 0 $，明确计算了自旋链哈密顿式的确切有限大小的地面特征值。在合适的归一化中，地下组件的特征是带有整数系数的$ x $中的多项式。该特征向量的线性总和规则和特殊组件是根据行列式公式明确计算的。这些结果从构建轮廓融合解决方案到与$ r $ -matrix和对角线$ k $ - 六个Vertex型号相关的边界量子量子knizhnik-zamolodchikov方程。该解决方案与完全对称交替的符号矩阵的加权枚举之间的关系。
The open XXZ spin chain with the anisotropy parameter $Δ=-\frac12$ and diagonal boundary magnetic fields that depend on a parameter $x$ is studied. For real $x>0$, the exact finite-size ground-state eigenvalue of the spin-chain Hamiltonian is explicitly computed. In a suitable normalisation, the ground-state components are characterised as polynomials in $x$ with integer coefficients. Linear sum rules and special components of this eigenvector are explicitly computed in terms of determinant formulas. These results follow from the construction of a contour-integral solution to the boundary quantum Knizhnik-Zamolodchikov equations associated with the $R$-matrix and diagonal $K$-matrices of the six-vertex model. A relation between this solution and a weighted enumeration of totally-symmetric alternating sign matrices is conjectured.
