  We show that a particular class of variational wave functions reproduces the
low-energy properties of the Hubbard model in one dimension. Our approach
generalizes to finite on-site Coulomb repulsion the fully-projected wave
function proposed by Hellberg and Mele [Phys. Rev. Lett. {\bf 67}, 2080 (1991)]
for describing the Luttinger-liquid behavior of the doped $t{-}J$ model. Within
our approach, the long-range Jastrow factor emerges from a careful minimization
of the energy, without assuming any parametric form for the long-distance tail.
Specifically, in the conducting phase of the Hubbard model at finite hole
doping, we obtain the correct power-law behavior of the correlation functions,
with the exponents predicted by the Tomonaga-Luttinger theory. By decreasing
the doping, the insulating phase is reached with a continuous change of the
small-$q$ part of the Jastrow factor.

Strongly Correlated Electrons