We analyze the nucleation of supersolid order out of the superfluid ground state of bosons on the triangular lattice. While the stability of supersolidity against phase separation in this system is by now well established for nearest-neighbor and long-range dipolar interactions, relevant for two-dimensional arrays of ultra-cold polar molecules, here we address directly the nature of the superfluid-to-supersolid transition. Based on symmetry arguments and quantum Monte Carlo simulations, we conclude that this quantum phase transition is driven first-order beyond the line of particle-hole symmetry. Along this line, the transition is continuous and its scaling behavior consistent with the three-dimensional (3D) XY universality class. We relate this finding to a 3D Z6 clock model description of the enlarged symmetry of the solid order parameter field. In the generic case however, the symmetry reduces to that of a 3D Z3 clock model, which reflects the first-order nature of the generic superfluid-to-supersolid quantum phase transition on the triangular lattice.
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