Spin-statistics relation and the Abelian braiding phase for anyons in fractional quantum Hall effect

Abstract

Quasihole excitations in fractional quantum Hall (FQH) systems exhibit fractional statistics and fractional spin, but how the spin-statistics relation emerges from many-body physics remains poorly understood. Here we prove a spin-statistics relation using only FQH wave functions, on both the sphere and disk geometry. In particular, the proof on the disk generalizes to all quasiholes in realistic systems, which have a finite size and could be deformed into arbitrary shapes. Different components of the quasihole spins are linked to different conformal Hilbert spaces (CHS), which are nullspaces of model Hamiltonians that host the respective FQH ground states and quasihole states. Understanding how the intrinsic spin of the quasiholes is linked to different CHS is crucial for the generalized spin-statistics relation that takes into account the effect of metric deformation. In terms of the experimental relevance, this enables us to study the effect of deformation and disorder that introduces an additional source of Berry curvature, an aspect of anyon braiding that has been largely neglected in previous literature.

5 pages, 4 figures, comments very welcome

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Cited by in corpus (5)

• Universal Modelling of Oscillations in Fractional Quantum Hall Fluids
• Robust translational invariance in topological bands against lattice potentials and disorders
• Laughlin's quasielectron as a non-local composite fermion
• Spin fractionalization at the edge of quantum Hall fluids induced by bulk quasiparticles
• Proposal for bulk measurement of braid statistics in fractional quantum Hall effect