  We present a local density approximation (LDA) for one-dimensional (1D)
systems interacting via the soft-Coulomb interaction based on quantum
Monte-Carlo calculations. Results for the ground-state energies and ionization
potentials of finite 1D systems show excellent agreement with exact
calculations, obtained by exploiting the mapping of an $N$-electron system in
$d$ dimensions, onto a single electron in $N\times d$ dimensions properly
symmetrized by the Young diagrams. We conclude that 1D LDA is of the same
quality as its three-dimensional (3D) counterpart, and we infer conclusions
about 3D LDA. The linear and non-linear time-dependent responses of 1D model
systems using LDA, exact exchange, and the exact solution are investigated and
show very good agreement in both cases, except for the well known problem of
missing double excitations. Consequently, the 3D LDA is expected to be of good
quality beyond linear response. In addition, the 1D LDA should prove useful in
modeling the interaction of atoms with strong laser fields, where this specific
1D model is often used.
