  A symmetrized Density Matrix Renormalization Group procedure together with
the correction vector approach is shown to be highly accurate for obtaining
dynamic linear and third order polarizabilities of one-dimensional Hubbard and
$U-V$ models. The $U-V$ model is seen to show characteristically different
third harmonic generation response in the CDW and SDW phases. This can be
rationalized from the excitation spectrum of the systems.
