  The one-dimensional extended t-V model of fermions on a lattice is a model
with repulsive interactions of finite range that exhibits a transition between
a Luttinger liquid conducting phase and a Mott insulating phase. It is known
that by tailoring the potential energy of the insulating system, one can force
a phase transition into another insulating phase. We show how to construct all
possible charge-density-wave phases of the system at low critical densities in
the atomic limit. Higher critical densities are investigated by a brute-force
analysis of the possible finite unit cells of the Fock states.
