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We analyze the nucleation of supersolid order out of the superfluid groundstate of bosons on the triangular lattice. While the stability of supersolidityagainst phase separation in this system is by now well established fornearest-neighbor and long-range dipolar interactions, relevant fortwo-dimensional arrays of ultra-cold polar molecules, here we address directlythe nature of the superfluid-to-supersolid transition. Based on symmetryarguments and quantum Monte Carlo simulations, we conclude that this quantumphase transition is driven first-order beyond the line of particle-holesymmetry. Along this line, the transition is continuous and its scalingbehavior consistent with the three-dimensional (3D) XY universality class. Werelate this finding to a 3D Z6 clock model description of the enlarged symmetryof the solid order parameter field. In the generic case however, the symmetryreduces to that of a 3D Z3 clock model, which reflects the first-order natureof the generic superfluid-to-supersolid quantum phase transition on thetriangular lattice.

Generic First-Order vs. Continuous Quantum Nucleation of Supersolidity