  We formulate a set of equations that facilitate an exact numerical solution
of the Kohn-Sham potential for a finite Hubbard chain with nearest neighbour
hopping and arbitrary site potentials. The approach relies on a mapping of the
non-interacting Kohn-Sham ground state wave function onto the exact interacting
system wavefunction and two interconnected self-consistent cycles. The
self-consistent cycles are performed within the framework of the Kohn-Sham
non-interacting system without any direct reference to the interacting system.
The first self-consistent cycle updates the mapping of the non-interacting
wavefunction onto the interacting wavefunction based on a trial input density,
while the second self-consistent cycle updates the Kohn-Sham potential to yield
the trial density. At the solution point, the exact density, the exact
Kohn-Sham potential, the density functional correlation energy and the exact
interacting system ground state energy are available.
