Braiding properties of paired spin-singlet and non-abelian hierarchy states

Abstract

We study explicit model wave functions describing the fundamental quasiholes in a class of non-abelian fractional quantum Hall states. This class is a family of paired spin-singlet states with $n\ge 1$ internal degrees of freedom. We determine the braid statistics of the quasiholes by determining the monodromy of the explicit quasihole wave functions, that is how they transform under exchanges of quasihole coordinates. The statistics is shown to be the same as that of the quasiholes in the Read-Rezayi states, up to a phase. We also discuss the application of this result to a class of non-abelian hierarchy wave functions.

arXiv comment32 pages; v2: references added

References in corpus (37)

• Anyons in an exactly solved model and beyond
• Topological orders and Edge excitations in FQH states
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Topologically-Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State
• $2n$ Quasihole States Realize $2^{n-1}$-Dimensional Spinor Braiding Statistics in Paired Quantum Hall States
• Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p_x+ip_y paired superfluids
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Quasiholes and fermionic zero modes of paired fractional quantum Hall states: the mechanism for nonabelian statistics
• Quantum Hall Physics - hierarchies and CFT techniques
• New Class of Non-Abelian Spin-Singlet Quantum Hall States
• Quantum groups and nonabelian braiding in quantum Hall systems
• Plasma Analogy and Non-Abelian Statistics for Ising-type Quantum Hall States
• Fractional Quantum Hall Hierarchy and the Second Landau Level
• Exact Matrix Product States for Quantum Hall Wave Functions
• Breaking of Particle-Hole Symmetry by Landau Level Mixing in the nu=5/2 Quantized Hall State
• Series of Abelian and Non-Abelian States in C>1 Fractional Chern Insulators
• Projective Construction of Non-Abelian Quantum Hall Liquids
• A modular functor which is universal for quantum computation
• Conformal invariance of chiral edge theories
• Braiding non-Abelian quasiholes in fractional quantum Hall states
• Topologically protected quantum gates for computation with non-Abelian anyons in the Pfaffian quantum Hall state
• Wavefunctions for topological quantum registers
• Quantum Hall states and boson triplet condensate for rotating spin-1 bosons
• Rotating spin-1 bosons in the lowest Landau level
• A Unified Conformal Field Theory Description of Paired Quantum Hall States
• Quantum Hall quasielectron operators in conformal field theory
• Non-Abelian Fractional Chern Insulators from Long-Range Interactions
• A Plasma Analogy and Berry Matrices for Non-Abelian Quantum Hall States
• Numerical study of charge and statistics of Laughlin quasi-particles
• Condensing non-Abelian quasiparticles
• Chiral correlators of the Ising conformal field theory
• Clebsch-Gordan and 6j-coefficients for rank two quantum groups
• Landau-Ginzburg Theories of Non-Abelian Quantum Hall States from Non-Abelian Bosonization
• Universality in Quantum Hall Systems: Coset Construction of Incompressible States
• On the anyon description of the Laughlin hole states
• Conformal field theory construction for nonabelian hierarchy wave functions

Cited by in corpus (2)

• Non-Hermitian skin clusters from strong interactions
• Exchange and exclusion in the non-abelian anyon gas