Extracting anyon statistics from neural network fractional quantum hall states
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Published version
Author(s)
Type
Journal Article
Abstract
Fractional quantum Hall states host emergent anyons with exotic exchange statistics, but obtaining direct access to their topological properties in real systems remains a challenge. Neural network wave functions provide a flexible computational approach, as they can represent highly correlated states without requiring a tailored basis. Here, we use the neural network variational Monte Carlo method to study the fractional quantum Hall effect on the torus and find the three degenerate ground states at filling factor 𝜈=1/3. From these, we extract the modular 𝑆
-matrix via entanglement interferometry, a technique previously only applied to lattice models. The resulting 𝑆
-matrix encodes the quantum dimensions, fusion rules, and exchange statistics of the emergent anyons, providing a direct numerical demonstration of the topological order. The calculated anyon properties match the well-known theoretical and experimental results. Our work establishes neural network wave functions as a powerful tool for investigating anyonic properties.
-matrix via entanglement interferometry, a technique previously only applied to lattice models. The resulting 𝑆
-matrix encodes the quantum dimensions, fusion rules, and exchange statistics of the emergent anyons, providing a direct numerical demonstration of the topological order. The calculated anyon properties match the well-known theoretical and experimental results. Our work establishes neural network wave functions as a powerful tool for investigating anyonic properties.
Date Issued
2026-09-08
Date Acceptance
2026-07-28
Citation
PRX Intelligence, 2026, 1 (1)
ISSN
3070-0329
Publisher
American Physical Society (APS)
Journal / Book Title
PRX Intelligence
Volume
1
Issue
1
Copyright Statement
Published by the American Physical Society Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
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Publication Status
Published
Article Number
013018
Date Publish Online
2026-09-08