Braiding Non-Abelian Quasiholes in Fractional Quantum Hall States

2014/05/31 by Yang-Le Wu, Benoit Estienne, B. Estienne +3 · 1 citation
Mathematics · Physics and Astronomy · #Abelian group #Anyon #Combinatorics #Electron #Fibonacci number #Fractional quantum Hall effect #Law #Mathematical physics #Mathematics #Physics #Political science #Quantum #Quantum Hall effect #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Quantum spin Hall effect #Realization (probability) #State (computer science) #Statistics #Topological Materials and Phenomena #Topological quantum computer #Unitary state #Wave function #cond-mat.str-el

paper · pdf · doi:10.1103/physrevlett.113.116801

published as Phys. Rev. Lett. 113, 116801 (2014) · 9 pages, 9 figures; published version

openalex publication_date 2014/09/08 · arxiv created 2014/09/09 · arxiv updated 2014/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

Quasiholes in certain fractional quantum Hall states are promising candidates for the experimental realization of non-Abelian anyons. They are assumed to be localized excitations, and to display non-Abelian statistics when sufficiently separated, but these properties have not been explicitly demonstrated except for the Moore-Read state. In this work, we apply the newly developed matrix product state technique to examine these exotic excitations. For the Moore-Read and the Z₃ Read-Rezayi states, we estimate the quasihole radii, and determine the correlation lengths associated with the exponential convergence of the braiding statistics. We provide the first microscopic verification for the Fibonacci nature of the Z₃ Read-Rezayi quasiholes. We also present evidence for the failure of plasma screening in the nonunitary Gaffnian wave function.

Citations

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Cited by

• Continuum limit of lattice models with Laughlin-like ground states containing quasiholes