  The fractional quantum Hall effect (FQHE) occurs at certain magnetic field
strengths B*(n) in a two-dimensional electron gas of density n at strong
magnetic fields perpendicular to the plane of the electron gas. At these
magnetic fields strengths, the system is incompressible, i.e., there is a
finite cost in energy for creating charge density fluctuations in the bulk,
while the boundary of the electron gas has gapless modes of density waves. The
bulk energy gap arises because of the strong electron-electron interactions.
While there are very good models for infinite homogeneous systems and for the
gapless excitations of the boundary of the electron gas, computational methods
to accurately model finite, inhomogeneous systems with more then about ten
electrons have not been available until very recently. We will here review an
ensemble density functional approach to studying the ground state of large
inhomogeneous spin polarized FQHE systems.
