Fractional charge pumping of anyons and the adiabatic heuristic principle

By using the Laughlin's argument on a torus with two pin-holes, the fractional charge pumping of anyons is numerically demonstrated. We have confirmed that the general feature of the energy spectra remains unchanged during the flux-attachment transformation of the adiabatic heuristic principle, even though the topological degeneracy is wildly changed. The total jump of the center-of-mass induced by the Laughlin's flux insertion works well as an invariant during this process. This result is consistent with the bulk-edge correspondence of the fractional quantum Hall effect of anyons [1].