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Recent experiments on ultracold dipoles in optical lattices open excitingpossibilities for the quantum simulation of extended Hubbard models. Whenconsidered in one dimension, these models present at unit filling aparticularly interesting ground-state physics, including a symmetry-protectedtopological phase known as Haldane insulator. We show that the tail of thedipolar interaction beyond nearest-neighbors, which may be tailored by means ofthe transversal confinement, does not only modify quantitatively the Haldaneinsulator regime and lead to density waves of larger periods, but results aswell in unexpected insulating phases. These insulating phases may betopological or topologically trivial, and are characterized by peculiarcorrelations of the site occupations. These phases may be realized and observedin state-of-the-art experiments.

Ground states of one-dimensional dipolar lattice bosons at unit filling