Anyonic Neural Network Wavefunctions
Abstract
The macroscopic behavior of a non-interacting gas of Abelian anyons has remained unsettled for many decades. Prior numerical methods employing exact diagonalization in the continuum and on the plane have been limited to small system sizes, at most N = 4 anyons. Using the rapidly developing technology of neural network wavefunctions, we develop variational ansatze appropriate for studying continuum models of the Abelian anyon gas. The neural network architecture, which we call "AnyNet", is capable of exactly enforcing the non-analytic short-distance behavior induced by the anyonic statistics. We demonstrate excellent agreement with exact diagonalization for N=4 anyons, obtain accurate results up to N = 16 for intermediate statistics, and study up to N=20 for almost-fermionic anyons, matching perturbative results within a 0.4% discrepancy. We use this methodology to study anyons in a harmonic trap, and anyonic atoms as a model for anyon binding to impurities. We study the structure of anyonic wavefunctions as the statistics parameter is varied. We focus on the single-particle density, the pair density, the angular momentum, and the scaling of the wavefunction as multiple anyons coalesce. This work opens doors to understanding the macroscopic behavior of anyons, for which rich phases have been predicted theoretically.
Related
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BibTeX
@misc{fadon2026anyonic,
title = {{Anyonic Neural Network Wavefunctions}},
author = {Andres Perez Fadon and Pok Man Tam and Leyna Shackleton},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23815},
eprint = {2610.23815},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23815},
}
RIS
TY - UNPB
TI - Anyonic Neural Network Wavefunctions
AU - Andres Perez Fadon
AU - Pok Man Tam
AU - Leyna Shackleton
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23815
UR - https://arxiv.org/abs/2610.23815
AB - The macroscopic behavior of a non-interacting gas of Abelian anyons has remained unsettled for many decades. Prior numerical methods employing exact diagonalization in the continuum and on the plane have been limited to small system sizes, at most N = 4 anyons. Using the rapidly developing technology of neural network wavefunctions, we develop variational ansatze appropriate for studying continuum models of the Abelian anyon gas. The neural network architecture, which we call "AnyNet", is capable of exactly enforcing the non-analytic short-distance behavior induced by the anyonic statistics. We demonstrate excellent agreement with exact diagonalization for N=4 anyons, obtain accurate results up to N = 16 for intermediate statistics, and study up to N=20 for almost-fermionic anyons, matching perturbative results within a 0.4% discrepancy. We use this methodology to study anyons in a harmonic trap, and anyonic atoms as a model for anyon binding to impurities. We study the structure of anyonic wavefunctions as the statistics parameter is varied. We focus on the single-particle density, the pair density, the angular momentum, and the scaling of the wavefunction as multiple anyons coalesce. This work opens doors to understanding the macroscopic behavior of anyons, for which rich phases have been predicted theoretically.
ER -