Quasiholes of 1/3 and 7/3 quantum Hall states: size estimates via exact diagonalization and density-matrix renormalization group

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We determine the size of the elementary quasihole in ν=1/3 and ν=7/3 quantum Hall states via exact-diagonalization and density-matrix renormalization group calculations on the sphere and cylinder, using a variety of short- and long-range pinning potentials. The size of the quasihole at filling factor ν=1/3 is estimated to be ≈ 4ℓB, and that of ν=7/3 is ≈ 7ℓB, where ℓB is the magnetic length. In contrast, the size of the Laughlin quasihole, expected to capture the basic physics in these two states, is around ≈ 2.5ℓB. Our work supports the earlier findings that the quasihole in the first excited Landau level is significantly larger than in the lowest Landau level.