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arXiv · 0709.2409

Skein Theory and Topological Quantum Registers: Braiding Matrices and Topological Entanglement Entropy of Non-Abelian Quantum Hall States

Kazuhiro Hikami
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Abstract

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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Kazuhiro Hikami. 2007-09-15. Skein Theory and Topological Quantum Registers: Braiding Matrices and Topological Entanglement Entropy of Non-Abelian Quantum Hall States. https://doi.org/10.1016/j.aop.2007.10.002

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