Quantum hexatic order in two-dimensional dipolar and charged fluids

Recent advances in cold atom experimentation suggest that studies of quantum two-dimensional melting of dipolar molecules, with dipoles aligned perpendicular to ordering plane, may be on the horizon. An intriguing aspect of this problem is that two-dimensional \emph{classical} aligned dipoles (already studied in great detail in soft matter experiments on magnetic colloids) are known to melt via a two-stage process, with an intermediate hexatic phase separating the usual crystal and isotropic fluid phases. We estimate here the effect of quantum fluctuations on this hexatic phase, for both dipolar systems and charged Wigner crystals. Our approximate phase diagrams rely on a pair of Lindemann criteria, suitably adapted to deal with effects of thermal fluctuations in two dimensions. As part of our analysis, we determine the phonon spectra of quantum particles on a triangular lattice interacting with repulsive $1/r^3$ and $1/r$ potentials. A large softening of the transverse and longitudinal phonon frequencies, due to both lattice effects and quantum fluctuations, plays a significant role in our analysis. The hexatic phase is predicted to survive down to very low temperatures.