The dark side of DFT based transport calculations

We compare the conductance of an interacting ring of six lattice sites threaded by flux $\pi$ in a two terminal setup with the conductance of the corresponding Kohn-Sham particles. Based on symmetry considerations we can show that even within (lattice) Density Functional Theory employing the exact Functional the conductance of the Kohn-Sham particles is exactly zero, while the conductance of the physical system is close to the unitary limit. We show that this fundamental problem might be solved by extending the standard DFT scheme.