Exact Kohn-Sham Density Functional Theory on a Lattice

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.