Braiding non-Abelian quasiholes in fractional quantum Hall states

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 ${\mathbb{Z}}_3$ 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 ${\mathbb{Z}}_3$ Read-Rezayi quasiholes. We also present evidence for the failure of plasma screening in the non-unitary Gaffnian wave function.

9 pages, 9 figures; published version

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Cited by in corpus (18)

• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Thirty Years of Composite Fermions and Beyond
• Microscopic Study of the Halperin - Laughlin Interface through Matrix Product States
• Anyon braiding in semi-analytical fractional quantum Hall lattice models
• Characterization of quasiholes in fractional Chern insulators
• Topological Interface between Pfaffian and anti-Pfaffian Order in $\nu =5/2$ Quantum Hall Effect
• Modular matrices from universal wave function overlaps in Gutzwiller-projected parton wave functions
• Matrix product state representation of non-Abelian quasiholes
• Taming Landau level mixing in fractional quantum Hall states with deep learning
• Model wavefunctions for interfaces between lattice Laughlin states
• Anyonic braiding via quench dynamics in fractional quantum Hall liquids
• Squeezing anyons for braiding on small lattices
• Conformal field theory approach to parton fractional quantum Hall trial wave functions
• Operator-state correspondence in simple current extended conformal field theories: Toward a general understanding of chiral conformal field theories and topological orders
• Conformal field theory construction for nonabelian hierarchy wave functions
• Anisotropy and quench dynamics of quasiholes in fractional quantum Hall liquids
• Spin fractionalization at the edge of quantum Hall fluids induced by bulk quasiparticles
• From the Gaffnian critical point to the incompressible 2/5 quantum Hall state