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

Abstract

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.