  The frequency-dependent response of a one-dimensional fermion system is
investigated using Current Density Functional Theory (CDFT) within the local
approximation (LDA). DFT-LDA, and in particular CDFT-LDA, reproduces very well
the dispersion of the collective excitations. Unsurprisingly, however, the
approximation fails for details of the dynamic response for large wavevectors.
In particular, we introduce CDFT for the one-dimensional spinless fermion model
with nearest-neighbor interaction, and use CDFT-LDA plus exact (Bethe ansatz)
results for the groundstate energy as function of particle density and boundary
phase to determine the linear response. The successes and failures of this
approach are discussed in detail.
