The macroscopic behavior of a non-interacting gas of Abelian anyons has remained unresolved for decades. Previous numerical methods, based on exact diagonalization in the continuum and on the plane, were limited to very small systems of at most N = 4 anyons. A new study explores neural network wavefunction technology to build variational ansätze suited to continuum models of the Abelian anyon gas.

The proposed architecture, dubbed "AnyNet", exactly enforces the non-analytic short-distance behavior induced by anyonic statistics. The method reproduces exact diagonalization results with excellent agreement for N = 4 anyons, reaches accurate results up to N = 16 for intermediate statistics, and extends to N = 20 for almost-fermionic anyons, with a 0.4% discrepancy relative to perturbative calculations.

Using this methodology, the authors study anyons in a harmonic trap and anyonic atoms as a model for anyon binding to impurities. They analyze the structure of anyonic wavefunctions as the statistics parameter is varied, focusing on the single-particle density, the pair density, the angular momentum, and the scaling of the wavefunction as multiple anyons coalesce.

The work opens the door to understanding the macroscopic behavior of anyons, for which rich phases have been predicted theoretically. Next steps will involve extending the method to larger system sizes and exploring those predicted phase transitions.