Statistics-Induced Topological States of Interacting Anyons

In the present paper, we examine the formation of topological edge states of pairs of interacting anyons. Such quantum particles obey specific generalized commutation relations interpolating between fermionic and bosonic ones and can be observed, for example, in the fractional quantum Hall effect. Considering a one-dimensional array of microresonators supporting anyonic excitations and connected with nearest neighbor tunneling couplings, we demonstrate that topological edge states can be observed. The presence and localization of these states at one of the array's edges is governed by the statistical exchange angle 0 < theta < pi, with limiting values 0 and pi corresponding to either bosons or pseudo-fermions, allowing us to address them as statistics-induced topological states.