Fractionally charged impurity states of a fractional quantum Hall system

The single-particle spectral function for an incompressible fractional quantum Hall state in the presence of a scalar short-ranged attractive impurity potential is calculated via exact diagonalization within the spherical geometry. In contrast to the noninteracting case, where only a single bound state below the lowest Landau level forms, electron-electron interactions strongly renormalize the impurity potential, effectively giving it a finite range, which can support many quasi-bound states (long-lived resonances). Averaging the spectral weights of the quasi-bound states and extrapolating to the thermodynamic limit, for filling factor $ν=1/3$ we find evidence consistent with localized fractionally charged $e/3$ quasiparticles. For $ν=2/5$, the results are slightly more ambiguous, due to finite size effects and possible bunching of Laughlin-quasiparticles.

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