Braiding statistics and congruent invariance of twist defects in bosonic bilayer fractional quantum Hall states

2013/08/27 by Jeffrey C. Y. Teo, Abhishek Roy, Xiao Chen +1 · 30 citations
Mathematics · Physics and Astronomy · #Anyon #Braid group #Charge (physics) #Degenerate energy levels #Electron #Geometry #Mathematics #Physics #Pure mathematics #Quantum #Quantum Hall effect #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Theoretical physics #Topological Materials and Phenomena #Topological order #Topological quantum computer #Toric code #Twist #cond-mat.str-el

paper · pdf · doi:10.1103/physrevb.90.155111

published in Physical Review B 90(15) (American Physical Society) · 6 pages, 3 figures

arxiv created 2013/08/27 · openalex publication_date 2014/10/08 · arxiv updated 2014/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

We describe the braiding statistics of topological twist defects in fractional quantum Hall (FQH) states. In particular, we study Abelian bosonic (mmn) FQH states with bilayer symmetries. Twist defects are staircases that lift orbiting quasiparticles from one layer to another. These point defects exhibit semiclassical non-Abelian characteristics. We develop a procedure to evaluate consistent basis transformations (F symbols) of the defect fusion theory. Unlike quantum anyonic excitations of a topological phase, the exchange and braiding statistics of twist defects is not characterized by modular transformations, but instead a subcollection known as congruent transformations. We also characterize the projective nature of unitary braiding operations and relate it to the global ℤ₂ bilayer symmetry.

Citations

• Fractional topological superconductor with fractionalized Majorana fermions
• TOPOLOGICAL ORDERS IN RIGID STATES
• 2n-quasihole states realize 2n−1-dimensional spinor braiding statistics in paired quantum Hall states
• Classification of Abelian quantum Hall states and matrix formulation of topological fluids
• Models for gapped boundaries and domain walls
• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Non-Abelian anyons and topological quantum computation
• Nonabelions in the fractional quantum hall effect
• Unpaired Majorana fermions in quantum wires
• Topological quantum computation

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