Fractionally charged bound states of an impurity in a fractional quantum Hall system

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