Anyon interactions in the Chern--Simons--Landau--Ginzburg model of the fractional quantum Hall effect

The interactions of anyonic quasi-particles (vortices) in the Chern--Simons extension of the Ginzburg--Landau model is investigated and we show that it manifestly realizes a hybridization of type I/II superconductivity. Through Gauss' law, each vortex simultaneously carries a flux quantum and a proportional Noether charge, thereby realizing an anyonic excitation. The Chern--Simons coupling also modifies the screening structure of the gauge fields, producing complex-conjugate masses that yield a common penetration depth with an oscillatory phase. This altered asymptotic behavior breaks the conventional type-I/type-II dichotomy of the Ginzburg--Landau model. As a result, vortex anyons experience short-range repulsion and long-range attraction, enabling the formation of separated multi-vortex bound states with non-monotonic interaction energy.