Ground state and edge excitations of a quantum Hall liquid at filling factor 2/3

We present a numerical study of fractional quantum Hall liquid at Landau-level filling factor nu=2/3 in a microscopic model including long-range Coulomb interaction and edge confining potential based on the disk geometry. We find that the ground state is accurately described by the particle-hole conjugate of a nu=1/3 Laughlin state. We also find that there are two counterpropagating edge modes, and the velocity of the forward-propagating mode is larger than the backward-propagating mode. The velocities have opposite responses to the change in the background confinement potential. On the other hand changing the two-body Coulomb potential has qualitatively the same effect on the velocities; for example, we find that increasing layer thickness (which softens of the Coulomb interaction) reduces both the forward mode and the backward mode velocities.