We present a theoretical study on the response properties to an external electric field of strongly correlated one-dimensional metals. Our investigation is based on the recently developed Bethe-Ansatz local density approximation (BALDA) to the density functional theory formulation of the Hubbard model. This is capable of describing both Luttinger liquid and Mott-insulator correlations. The BALDA calculated values for the static linear polarizability are compared with those obtained by numerically accurate methods, such as exact (Lanczos) diagonalization and the density matrix renormalization group, over a broad range of parameters. In general BALDA linear polarizabilities are in good agreement with the exact results. The response of the exact exchange and correlation potential is found to point in the same direction of the perturbing potential. This is well reproduced by the BALDA approach, although the fine details depend on the specific parameterization for the local approximation. Finally we provide a numerical proof for the non-locality of the exact exchange and correlation functional.
