  We study a system of electrons on a one-dimensional lattice, interacting
through the long range Coulomb forces, by means of a variational technique
which is the strong coupling analog of the Gutzwiller approach. The problem is
thus the quantum version of Hubbard's classical model of the generalized Wigner
crystal [J. Hubbard, Phys. Rev. B 17, 494 (1978)]. The magnetic exchange energy
arising from quantum fluctuations is calculated, and turns out to be smaller
than the energy scale governing charge degrees of freedom. This approach could
be relevant in insulating quasi-one-dimensional compounds where the long range
Coulomb interactions are not screened. In these compounds charge order often
appears at high temperatures and coexists with magnetic order at low
temperatures.
