Effect of the Soliton Width on Nonequilibrium Exchange Phases of Anyons

Unlike bosons and fermions, quasi-particles in two-dimensional quantum systems, known as anyons, exhibit exchange statistics intermediate between bosons and fermions. In fractional quantum Hall states, these anyons possess a fraction of the electron charge, and exchanging two anyons results in an exchange phase θ. While the fractional charge was measured some time ago, direct evidence for the anyonic statistical phase has only been found recently. In fractional quantum Hall devices, anyons propagate along chiral edge channels. By coupling different edge channels through a quantum point contact, anyon colliders can be constructed, enabling the observation of two-particle interference effects. Such configurations are instrumental in deducing the anyonic exchange phase via current cross-correlations. Prior theoretical models represented dilute anyon beams as discrete steps in the boson fields. However, our study reveals that incorporating the finite width of the soliton shape is crucial for accurately interpreting recent experiments, especially for collider experiments involving anyons with exchange phases θ>π/2, where previous theories fall short. We demonstrate that incorporating a finite soliton width leads to a prediction of negative Fano factors for anyons with exchange phases of 3π/5, in agreement with recent experimental data. In addition, we describe the dependence of the experimentally accessible Fano factor on the dynamical exponent, which governs the power law decay of the anyonic correlation functions, and on the current imbalance between the incident beams.