  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.
