Skein理论与拓扑量子寄存器：非阿贝尔量子Hall态的编织矩阵和拓扑纠缠熵
Skein Theory and Topological Quantum Registers: Braiding Matrices and Topological Entanglement Entropy of Non-Abelian Quantum Hall States
摘要：
研究了非阿贝尔量子霍尔态中准粒子态的拓扑性质。我们对Read-Rezayi态应用了一种自旋理论方法，其有效理论是SU（2）_KChern-Simons理论。作为Pfronan（K=2）和Fibonacci（K=3）任意子态的推广，我们计算了具有任意自旋的准粒子态的编织矩阵.此外，我们提出了一种方法来计算的纠缠熵skein理论。我们发现纠缠熵有一个非平凡的贡献，称为拓扑纠缠熵，它依赖于非阿贝尔准粒子纠缠两个子系统的量子维数。
英文摘要：
We study topological properties of quasi-particle states in the non-Abelian quantum Hall states. We apply a skein-theoretic method to the Read--Rezayi state whose effective theory is the SU(2)_K Chern--Simons theory. As a generalization of the Pfaffian (K=2) and the Fibonacci (K=3) anyon states, we compute the braiding matrices of quasi-particle states with arbitrary spins. Furthermore we propose a method to compute the entanglement entropy skein-theoretically. We find that the entanglement entropy has a nontrivial contribution called the topological entanglement entropy which depends on the quantum dimension of non-Abelian quasi-particle intertwining two subsystems.
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