I discuss the phase diagram of spinless bosons with long range (~1/r
repulsive interactions relevant to ultracold polarized atoms or molecules.
Using the density matrix renormalization group we find a new insulating phase
between the two conventional insulators: Mott and density wave phases. The
new phase is characterized by hidden topological order that is revealed only
by nonlocal string correlations analogous to those characterizing the Haldane
gapped phase of integer spin chains.
To predict experimental signatures of the new phase we develop an effective low energy theory that describes the elementary excitations and use it to calculate the absorption spectrum due to oscillatory lattice modulation and Bragg spectroscopy. We predict a sharp resonance in the spectrum due to a collective excitation of the new phase that would provide clear evidence for the existence of this phase.