Skein theory and topological quantum registers: Braiding matrices and topological entanglement entropy of non-Abelian quantum Hall states

2007/09/15 by Kazuhiro Hikami · 2 citations
Physics and Astronomy · #Quantum and electron transport phenomena #Quantum many-body systems #Topological Materials and Phenomena #quant-ph

paper · pdf · doi:10.1016/j.aop.2007.10.002

published as Annals of Physics 323, 1729-1769 (2008) · 42 pages, many eps files

arxiv created 2007/09/15 · openalex publication_date 2007/11/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

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.

Citations

• Current algebra and Wess-Zumino model in two dimensions
• Topological quantum compiling
• Quantum Phases of Vortices in Rotating Bose-Einstein Condensates
• String-net condensation: A physical mechanism for topological phases
• Invariants of 3-manifolds via link polynomials and quantum groups
• Interferometry of non-Abelian Anyons
• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Non-Abelian Anyons and Topological Quantum Computation
• Nonabelions in the fractional quantum hall effect
• Classical and quantum conformal field theory
• Entanglement in many-body systems

Cited by

• Direct experimental simulation of the Yang–Baxter equation
• Information-theoretical formulation of anyonic entanglement