Quasiholes of 13 and 73 quantum Hall states: Size estimates via exact diagonalization and density-matrix renormalization group

Abstract

We determine the size of the elementary quasihole in =1/3 and =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 =1/3 is estimated to be 4,"B, and that of =7/3 is 7,"B, where ,"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 2.5, "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.