Continuum neural wavefunctions for anyons on a torus
Abstract
Mobile anyons in topologically ordered phases provide a setting to investigate how fractional exchange statistics shapes collective behavior at finite density. We introduce AnyFormer: a neural variational framework for continuum anyons on a torus that explicitly incorporates statistical interactions and global winding constraints. We construct a smooth orbital frame that enforces the matrix-valued torus boundary conditions, and supplement it with an analytic pair factor that supplies the regular collision behavior. The orbital geometry and many-body amplitudes are optimized in parallel by variational Monte Carlo. We apply AnyFormer to semions without an external field or interaction potential, isolating unique correlations generated solely by statistics. Our framework closely matches exact two-semion energies and yields lower variational energies than finite-cutoff exact diagonalization for N = 4 and $6$ semions. Scaling up to N = 16 semions, well beyond the limits of continuum diagonalization, we find a largely uniform liquid with pronounced correlation holes and an approximately linear structure factor at the smallest accessible wavevectors. The pair circulation reverses near the mean particle spacing, revealing chiral relative motion. We then identify paired superfluid behavior through spatially persistent coherence of compact semion pairs, carried by a counter-rotating pair channel. The ansatz is not biased toward pairing, so this result emerges from energy minimization alone. AnyFormer thus provides a scalable variational neural-net framework for microscopic studies of correlations, chiral motion, and collective phases of bulk anyonic matter.
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BibTeX
@misc{khalifa2026continuum,
title = {{Continuum neural wavefunctions for anyons on a torus}},
author = {Ahmed Khalifa and Shubhayu Chatterjee},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36567},
eprint = {2610.36567},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36567},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Continuum neural wavefunctions for anyons on a torus
AU - Ahmed Khalifa
AU - Shubhayu Chatterjee
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.36567
UR - https://arxiv.org/abs/2610.36567
AB - Mobile anyons in topologically ordered phases provide a setting to investigate how fractional exchange statistics shapes collective behavior at finite density. We introduce AnyFormer: a neural variational framework for continuum anyons on a torus that explicitly incorporates statistical interactions and global winding constraints. We construct a smooth orbital frame that enforces the matrix-valued torus boundary conditions, and supplement it with an analytic pair factor that supplies the regular collision behavior. The orbital geometry and many-body amplitudes are optimized in parallel by variational Monte Carlo. We apply AnyFormer to semions without an external field or interaction potential, isolating unique correlations generated solely by statistics. Our framework closely matches exact two-semion energies and yields lower variational energies than finite-cutoff exact diagonalization for N = 4 and $6$ semions. Scaling up to N = 16 semions, well beyond the limits of continuum diagonalization, we find a largely uniform liquid with pronounced correlation holes and an approximately linear structure factor at the smallest accessible wavevectors. The pair circulation reverses near the mean particle spacing, revealing chiral relative motion. We then identify paired superfluid behavior through spatially persistent coherence of compact semion pairs, carried by a counter-rotating pair channel. The ansatz is not biased toward pairing, so this result emerges from energy minimization alone. AnyFormer thus provides a scalable variational neural-net framework for microscopic studies of correlations, chiral motion, and collective phases of bulk anyonic matter.
ER -