Plasma analogy and non-Abelian statistics for Ising-type quantum Hall states

Journal Article · Tue Feb 15 00:00:00 EST 2011 · Physical Review. B, Condensed Matter and Materials Physics

DOI:https://doi.org/10.1103/PHYSREVB.83.075303· OSTI ID:21538127

Bonderson, Parsa ^[1]; Gurarie, Victor ^[2]; Nayak, Chetan ^[1]

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1. Microsoft Station Q, Elings Hall, University of California at Santa Barbara, Santa Barbara, California 93106 (United States)
2. Department of Physics, CB390, University of Colorado, Boulder, Colorado 80309 (United States)

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 {nu}=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.

• OSTI ID: 21538127
• Journal Information: Physical Review. B, Condensed Matter and Materials Physics, Vol. 83, Issue 7; Other Information: DOI: 10.1103/PhysRevB.83.075303; (c) 2011 American Institute of Physics; ISSN 1098-0121
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
CONFORMAL INVARIANCE
CORRELATION FUNCTIONS
ELECTRIC CONDUCTIVITY
EXCITATION
ISING MODEL
PLASMA
QUANTUM FIELD THEORY
QUANTUM STATES
QUASI PARTICLES
STATISTICS
WAVE FUNCTIONS
CRYSTAL MODELS
ELECTRICAL PROPERTIES
ENERGY-LEVEL TRANSITIONS
FIELD THEORIES
FUNCTIONS
INVARIANCE PRINCIPLES
MATHEMATICAL MODELS
MATHEMATICS
PHYSICAL PROPERTIES