We study the quantum melting of quasi-one-dimensional lattice models in which
the dominant energy scale is given by a repulsive dipolar interaction. By
constructing an effective low-energy theory, we show that the melting of
crystalline phases can occur into two distinct liquid phases, having the same
algebraic decay of density-density correlations, but showing a different
non-local correlation function expressing string order. We present possible
experimental realizations using ultracold atoms and molecules, introducing an
implementation based on resonantly driven Rydberg atoms that offers additional
benefits compared to a weak admixture of the Rydberg state.Comment: 6 pages, 4 figure
