  We apply reduced density-matrix functional theory to the parabolically
confined quantum Hall droplet in the spin-frozen strong magnetic field regime.
One-body reduced density matrix functional method performs remarkably well in
obtaining ground states, energies, and observables derivable from the one-body
reduced density matrix for a wide range of system sizes. At the strongly
correlated regime, the results go well beyond what can be obtained with the
density functional theory. However, some of the detailed properties of the
system, such as the edge Green's function, are not produced correctly unless we
use the much heavier two-body reduced density matrix method.
