Chern-Simons Theory and Non-Abelian Anyons in Fractional Quantum Hall States — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Chern-Simons theory at level \(k\) governs fractional quantum Hall anyons; braiding produces non-abelian phases encoded in the Jones polynomial; lattice realizations confirm topological invariance; a novel CKM angle measurement is unrelated to topological physics. MATH: Chern-Simons action \(S_{CS} = \frac{k}{4\pi}\int \text{Tr}(A\wedge dA + \frac{2}{3}A\wedge A\wedge A)\); level \(k \in \mathbb{Z}\) (integer QHE) or \(k = p/q\) (fractional QHE, e.g., \(k=1/3\) for Laughlin state); anyon braiding phase \(\theta = \pi/k\) (abelian) or unitary matrix \(U_{ab}\) (non-abelian, e.g., Fibonacci anyons with \(U \sim e^{i\pi/5}\)); entanglement entropy \(S_A = \alpha L - \gamma\), with topological entanglement entropy \(\gamma = \ln \sqrt{D}\), \(D = \sum_i d_i^2\) (quantum dimensions); lattice Chern-Simons reproduces continuum in limit \(a \to 0\) with \(k\) quantized. CONNECTION: Level \(k=5\) gives Fibonacci anyons with quantum dimension \(d = \phi = 1.618\) (golden ratio) — di Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221506907
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