从多任意子Pfronan波函数坐标交换Ising任意子的最终辫群生成元
Ultimate braid-group generators for coordinate exchanges of Ising anyons from the multi-anyon Pfaffian wave functions
摘要：
我们给出了一个严格的和自洽的基本辫子矩阵表示的交换相邻伊辛任意子在两个不等价的表示的Pfronan量子霍尔态与偶数和奇数的马约拉纳费米子。为此，我们使用不同的算子乘积展开的手征自旋场的Neveu-Schwarz和Ramond部门的二维伊辛共形场论。我们发现递归关系的不可约表示的辫子群B_{2n+2}的发电机在那些为B_{2n}，以及明确的公式，几乎所有的辫子矩阵交换伊辛任意子。最后证明了由多任意子Pfronan波函数得到的辫子群表示与SO（2n+2）的旋量表示完全等价，并给出了等价矩阵.这实际上证明了2n个手征伊辛自旋场σ的关联函数确实实现了Nayak和Wilczek所提出的转动群SO（2n）的两个不等价旋量表示之一。
英文摘要：
We give a rigorous and self-consistent derivation of the elementary braid matrices representing the exchanges of adjacent Ising anyons in the two inequivalent representations of the Pfaffian quantum Hall states with even and odd number of Majorana fermions. To this end we use the distinct operator product expansions of the chiral spin fields in the Neveu-Schwarz and Ramond sectors of the two-dimensional Ising conformal field theory. We find recursive relations for the generators of the irreducible representations of the braid group B_{2n+2} in terms of those for B_{2n}, as well as explicit formulas for almost all braid matrices for exchanges of Ising anyons. Finally we prove that the braid-group representations obtained from the multi-anyon Pfaffian wave functions are completely equivalent to the spinor representations of SO(2n+2) and give the equivalence matrices explicitly. This actually proves that the correlation functions of 2n chiral Ising spin fields sigma do indeed realize one of the two inequivalent spinor representations of the rotation group SO(2n) as conjectured by Nayak and Wilczek.
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