Exact ground state density functional theory for impurity models coupled to external reservoirs and transport calculations

A method is presented, which employs the density matrix renormalization group technique in order to construct exact ground state exchange correlation functionals for models of correlated electron systems coupled to external reservoirs. The technique is applied to the M-site resonant level model. We calculate its exact Kubo-conductance, which is available within DMRG, and compare to the single-particle conductance obtained from Kohn-Sham energies and orbitals of the exact ground state density functional theory (DFT). It is found that the position of transport resonances is reproduced essentially exactly, while deviations in the level broadening can be less than 1% and do not exceed 10%. Our findings lend strong support to a recently held point of view, namely that approximations in the ground state functionals used in DFT based transport calculations can lead to drastic errors in transport calculations while exchange correlation contributions to the induced effective potential tend to be less significant.