Tunable Anyon Molecules in Quantum Hall Antidots Probe Non-Abelian Braiding — E8 Intelligence Research

Andrew Stewart Caldin

Published Nov 1, 2026• 0 citations

Abstract

FINDING: Moore-Read Pfaffian anyons in quantum Hall antidots form tunable "anyon molecules" whose tunneling spectroscopy probes non-Abelian braiding statistics | MATH: ν=5/2 FQH state; Pfaffian wavefunction Ψ = Pf(1/(z_i−z_j))·∏(z_i−z_j)^2·exp(−Σ|z_i|²/4); quasiparticle charge e/4; non-Abelian Ising anyons σ with fusion σ×σ = 1 + ψ | CONNECTION: Ising anyon fusion rules map to SU(2)₂ WZW model; conformal weights h_σ = 1/16, h_ψ = 1/2; modular S-matrix S = (1/√2)[[1,1],[1,−1]] — identical to the Hadamard gate, linking to golden-ratio-free but crystallographic A₁ root system | DEPTH: 9 FINDING: Universal anyon tunneling in chiral Luttinger liquid confirms power-law scaling independent of microscopic details | MATH: Tunneling density of states ∝ ω^(1/ν − 1); for ν=1/3, exponent = 2; for ν=5/2, effective exponent governed by e/4 quasiparticle; chiral Luttinger parameter g = ν | CONNECTION: Exponent 1/ν − 1 yields 2 for ν=1/3 — integer, reflecting SU(3)₁ structure; ν=5/2 gives 1/ν−1 = −3/5 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.23853663

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