论文标题
超对称八个Vertex模型的总和规则
Sum rules for the supersymmetric eight-vertex model
论文作者
论文摘要
具有顶点权重$ a，b，c，d $遵守关系$（a^2+ab）（b^2+ab）（b^2+ab）=（c^2+ab）（d^2+ab）$的八个vertex模型。其传输矩阵，具有$ L = 2n+1，\，n \ geqslant 0，$垂直线和沿水平方向的周期性边界条件具有双重成分特征值$θ_n=（a+b）^{2n+1} $。研究了相应的特征空间的基础。涉及基础向量的几种标量产品是根据Rosengren和Zinn-Justin引入的多项式家族计算的。这些标量产品用于查找向量特定条目的明确表达式。这些结果的证明是基于$θ_n$的特征值问题对不均匀八个Vertex模型的概括。
The eight-vertex model on the square lattice with vertex weights $a,b,c,d$ obeying the relation $(a^2+ab)(b^2+ab)=(c^2+ab)(d^2+ab)$ is considered. Its transfer matrix with $L=2n+1,\, n\geqslant 0,$ vertical lines and periodic boundary conditions along the horizontal direction has the doubly-degenerate eigenvalue $Θ_n = (a+b)^{2n+1}$. A basis of the corresponding eigenspace is investigated. Several scalar products involving the basis vectors are computed in terms of a family of polynomials introduced by Rosengren and Zinn-Justin. These scalar products are used to find explicit expressions for particular entries of the vectors. The proofs of these results are based on the generalisation of the eigenvalue problem for $Θ_n$ to the inhomogeneous eight-vertex model.
