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.1 Introduction Density Functional Theory (DFT) is an efficient and powerful tool for determining the electronic structure of solids. While originally developed for continuum electron systems with Coulomb interaction [1,2], DFT has also been applied to lattice models, such as the Hubbard model [3][4][5][6], in order to develop new approaches to correlated electron systems: lattice models often allow for exact solutions which hence can serve as benchmarks for assessing the quality of approximations.Very useful for applications is the Local Density Approximation (LDA) where the exchange-correlation energy of the inhomogeneous system under consideration is constructed via a local approximation from the homogeneous electron system. A lattice version of LDA has been suggested for one-dimensional systems [5] where the underlying homogeneous system can be solved using Bethe ansatz. For recent applications of Bethe ansatz LDA, see also, for example, Refs. [6][7][8][9][10][11][12].In addition, the time-dependent version of DFT has been developed and applied [13,14], in particular, the current density version [15]; a recent review [16] and book [17] provide excellent overviews, including the relation to standard many-body Green's function approaches.In this article, we focus on the one-dimensional spinless fermion model with nearest-neighbor interaction, which is exactly solvable in the homogeneous case [19,20]. We extend our recent DFT-LDA approach [18] to current den-