  Recent experiments on ultracold dipoles in optical lattices open exciting
possibilities for the quantum simulation of extended Hubbard models. When
considered in one dimension, these models present at unit filling a
particularly interesting ground-state physics, including a symmetry-protected
topological phase known as Haldane insulator. We show that the tail of the
dipolar interaction beyond nearest-neighbors, which may be tailored by means of
the transversal confinement, does not only modify quantitatively the Haldane
insulator regime and lead to density waves of larger periods, but results as
well in unexpected insulating phases. These insulating phases may be
topological or topologically trivial, and are characterized by peculiar
correlations of the site occupations. These phases may be realized and observed
in state-of-the-art experiments.
