Edge excitations and non-abelian statistics in the moore-read state: A numerical study in the presence of Coulomb interaction and edge confinement

We study the ground state and low-energy excitations of fractional quantum Hall systems on a disk at a filling fraction v = 5/2, with Coulomb interaction and a background confining potential. We find the Moore-Read ground state is stable within a finite but narrow window in parameter space. The corresponding low-energy excitations contain a fermionic branch and a bosonic branch, with widely different velocities. A short-range repulsive potential can stabilize a charge + e/4 quasihole at the center, leading to a different edge excitation spectrum due to the change of boundary conditions for Majorana fermions, clearly indicating the non-Abelian nature of the quasihole.