Statistical Anyons in 1D via Dispersion Engineering

We show that the single-particle dispersion relation can serve as a tuning knob for the exclusion statistics of particles. Specifically, we investigate one-dimensional hard-core bosons with a dispersion ε(k) ∝k^m, where m is an even integer greater than 2. This class of models is integrable and admits Bethe-ansatz solutions. The system exhibits m-dependent fractional exclusion statistics and many-body wavefunctions analogous to Laughlin states in fractional quantum Hall systems. Finally, we outline how this physics can be realized and tested experimentally using ultracold atoms in shaken optical lattices or atomic array platforms with tunable hopping amplitudes.