### 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.

Original language | English |
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Pages (from-to) | 1729-1769 |

Number of pages | 41 |

Journal | Annals of Physics |

Volume | 323 |

Issue number | 7 |

DOIs | |

Publication status | Published - Jul 1 2008 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

**Skein theory and topological quantum registers : Braiding matrices and topological entanglement entropy of non-Abelian quantum Hall states.** / Hikami, Kazuhiro.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Skein theory and topological quantum registers

T2 - Braiding matrices and topological entanglement entropy of non-Abelian quantum Hall states

AU - Hikami, Kazuhiro

PY - 2008/7/1

Y1 - 2008/7/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=44649128027&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=44649128027&partnerID=8YFLogxK

U2 - 10.1016/j.aop.2007.10.002

DO - 10.1016/j.aop.2007.10.002

M3 - Article

VL - 323

SP - 1729

EP - 1769

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

IS - 7

ER -