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We prove a generic spin-statistics relation for the fractional quasiparticles that appear in quantum Hall planar setups. The proof is based on an efficient way for computing the Berry phase acquired by a generic quasiparticle translated in the plane along a circular path, and on the crucial fact that once the gauge-invariant generator of rotations is projected onto a Landau level, it fractionalizes among the quasiparticles and the edge. Using these results we define a measurable quasiparticle fractional spin that satisfies the spin-statistics relation. As an application, we predict the value of the spin of the composite-fermion quasielectron proposed by Jain; our numerical simulations agree with that value. We also show that the difficulties encountered when studying the statistical properties of Laughlin’s quasielectron can be traced back to a spin that does not satisfy the spin- statistics relation. We conclude with some remarks on the total angular momentum of the system as a function of the quasiparticle positions and on an ambiguity in the definition of the spin. Further results on the non-Abelian anyons of the Moore-Read wavefunction will be presented. References [1] A. Nardin, E. Ardonne and LM, unpublished [2] Comparin, Biella, Opler, Macaluso, Polychronakos, LM, PRB 105 085125 (2022) [3] Macaluso, Comparin, LM, Carusotto, PRL 123 266801 (2020)

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Leonardo Mazza, LPTMS - Université Paris-Saclay
Seminar Room 0.03, ETP
Contact: Matteo Rizzi