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

We determine the size of the elementary quasihole in $\nu=1/3$ and $\nu=7/3$

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 $\nu=1/3$ is estimated to be $\approx 4\ell_B$, and that of

$\nu=7/3$ is $\approx 7\ell_B$, where $\ell_B$ is the magnetic length. In

contrast, the size of the Laughlin quasihole, expected to capture the basic

physics in these two states, is around $\approx 2.5\ell_B$. Our work supports

the earlier findings that the quasihole in the first excited Landau level is

significantly larger than in the lowest Landau level.