  One-dimensional polar gases in deep optical lattices present a severely
constrained dynamics due to the interplay between dipolar interactions, energy
conservation, and finite bandwidth. The appearance of dynamically-bound
nearest-neighbor dimers enhances the role of the $1/r^3$ dipolar tail,
resulting, in the absence of external disorder, in quasi-localization via dimer
clustering for very low densities and moderate dipole strengths. Furthermore,
even weak dipoles allow for the formation of self-bound superfluid lattice
droplets with a finite doping of mobile, but confined, holons. Our results,
which can be extrapolated to other power-law interactions, are directly
relevant for current and future lattice experiments with magnetic atoms and
polar molecules.

Quantum Gases;Statistical Mechanics;Strongly Correlated Electrons