Density oscillation of Laughlin Quasihole

Quasiholes are emergent elementary particles in the fractional quantum Hall effect. Due to the correlation between electrons, they are not point objects but extended ones which exhibit rich internal structures. In this work, we show that the complex density distribution of Laughlin quasiholes in real space can be modeled with a simple damped oscillation in the occupation-number space, which are fully determined by two characteristic length scales, the decay length and oscillation wave vector. In this way, the Laughlin quasihole, Laughlin edge and the pair correlation function of Laughlin ground state can be studied on an equal footing. Moreover, by tuning the interaction from the parent Hamiltonian to Coulomb interaction, we find the density oscillation of quasihole will be primarily modified by the low-energy quasihole-magnetoroton states, leading to an additional pair of oscillation and decay length for more realistic quasiholes in the experiments. Our results can also be useful for the large scale numerical computation of ground state and quasihole state variational energies.