Exact Solutions Of A Model For Synthetic Anyons In A Noninteracting System

We study a theoretical model for synthetic anyons in a noninteracting quantum many-body system. Synthetic anyons can occur in a noninteracting system when it is perturbed with specially tailored localized probes, which supply the demanded nontrivial topology in the system. The model is represented by the Hamiltonian for noninteracting electrons in two dimensions, in a uniform magnetic field, pierced with solenoids with a magnetic flux that is a fraction of the flux quantum. In a potential experimental realization of the model, there should be a mechanism fixing the flux in all solenoid probes to an identical value for these perturbations to represent synthetic anyons. We find analytically and numerically the ground state of the model when only the lowest Landau-level states are occupied. We calculate the statistical parameter by using the Berry phase, and show that the ground state is anyonic in the coordinates of the probes. We show that these synthetic anyons cannot be considered as emergent quasiparticles. The fusion rules are discussed for different microscopic realizations of the fusion process.