Anyons are particles with fractional statistics — neither bosons nor fermions, but something in between. In two dimensions, they are theoretically central to topological quantum computing and have been realized in quantum Hall systems. In one dimension, their existence has been predicted but debated, with exotic many-body phases expected but never directly observed.
Béguin and colleagues (arXiv:2602.20421) prepare two-body ground states of the one-dimensional anyon-Hubbard model using ultracold atoms in an optical lattice. The technique: Hamiltonian engineering through quasiperiodic drives combined with adiabatic state preparation. Two effects emerge.
First, pseudo-fermionization — anyons in one dimension behave increasingly like fermions as the statistical parameter approaches the fermionic limit, even though the underlying particles are bosons. The statistical interaction creates effective exclusion without the Pauli principle. The system imports fermionic behavior from the phase accumulated during exchange.
Second, chiral bound states — when two anyons remain close together, they form bound pairs whose properties depend on the direction of relative motion. Left and right are not equivalent. The chirality comes directly from the fractional statistics: the phase acquired during exchange breaks time-reversal symmetry for the pair, making the bound state asymmetric.
These results connect lattice models to continuum anyon theories and mark the first experimental signatures of statistical interactions in 1D anyonic systems.
The general observation: the properties of composite objects (bound pairs) can have lower symmetry than the system's Hamiltonian. The fractional statistics parameter breaks a symmetry — chirality — that the bare interaction preserves. The bound state inherits the broken symmetry from the exchange phase, not from the potential.