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.

• Received 21 October 2013
• Revised 28 January 2014

DOI:https://doi.org/10.1103/PhysRevB.89.115124