  Ultracold dipolar hard-core bosons in optical ladders provide exciting
possibilities for the quantum simulation of anisotropic XXZ spin ladders. We
show that introducing a tilt along the rungs results in a rich phase diagram at
unit filling. In particular, for a sufficiently strong dipolar strength, the
interplay between the long-range tail of the dipolar interactions and the
tilting leads to the emergence of a quantum floating phase, a critical phase
with incommensurate density-density correlations. Interestingly, the study of
the entanglement spectrum, reveals that the floating phase is topological,
constituting an intermediate gapless stage in the melting of a crystal into a
gapped topological Haldane phase. This novel scenario for topological floating
phases in dipolar XXZ ladders can be investigated in on-going experiments.
