Extracting Anyon Statistics from Neural Network Fractional Quantum Hall States
Year: 2026
Type: 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.
Source: PRX Intelligence
DOI: 10.1103/sb8g-qvn6
Authors: Andres Perez Fadon, David Pfau, James S. Spencer, Wan Tong Lou, Titus Neupert, W. M. C. Foulkes
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Funders: Jülich Supercomputing Centre, Forschungszentrum Jülich, UK Research and Innovation, European Commission, Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung, Engineering and Physical Sciences Research Council, Science and Technology Facilities Council, Department for Science, Innovation and Technology
OpenAlex ID: W4417534082