Successes and failures of Bethe ansatz density functional theory

The response of a one-dimensional fermion system is investigated using density functional theory (DFT) within the local-density approximation (LDA) and compared with exact results. It is shown that DFT-LDA reproduces surprisingly well some of the characteristic features of the Luttinger liquid, for example, the dispersion of the collective charge excitations. On the other hand, the approximation fails even qualitatively for details of the dynamic response and for quantities for which backscattering is important, i.e., those quantities which are crucial for an accurate description of transport. In particular, the Drude weight in the presence of a single impurity is discussed.