2010/08/31 by Parsa Bonderson, Victor Gurarie, Chetan Nayak · 1 citation
Mathematics · Physics and Astronomy · #Conformal field theory #Conformal map #Ising model #Magnetic field #Mathematical analysis #Mathematical physics #Mathematics #Pfaffian #Physics #Physics of Superconductivity and Magnetism #Pure mathematics #Quantum Hall effect #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Wave function #cond-mat.mes-hall #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1103/physrevb.83.075303
published as Phys. Rev. B 83, 075303 (2011) · 68 pages, 3 figures; v2: substantial revisions and additions for clarity, minor corrections
arxiv created 2011/02/02 · openalex publication_date 2011/02/07 · arxiv updated 2013/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the non-Abelian statistics of quasiparticles in the Ising-type quantum Hall states which are likely candidates to explain the observed Hall conductivity plateaus in the second Landau level, most notably the one at filling fraction \ensuremathν=5/2. We complete the program started in V. Gurarie and C. Nayak, [Nucl. Phys. B 506, 685 (1997)]. and show that the degenerate four-quasihole and six-quasihole wave functions of the Moore-Read Pfaffian state are orthogonal with equal constant norms in the basis given by conformal blocks in a c=1+(1)/(2) conformal field theory. As a consequence, this proves that the non-Abelian statistics of the excitations in this state are given by the explicit analytic continuation of these wave functions. Our proof is based on a plasma analogy derived from the Coulomb gas construction of Ising model correlation functions involving both order and (at most two) disorder operators. We show how this computation also determines the non-Abelian statistics of collections of more than six quasiholes and give an explicit expression for the corresponding conformal block-derived wave functions for an arbitrary number of quasiholes. Our method also applies to the anti-Pfaffian wave function and to Bonderson-Slingerland hierarchy states constructed over the Moore-Read and anti-Pfaffian states.