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We analyse the ground-state quantum phase diagram of hardcore Bosonsinteracting with repulsive dipolar potentials. The bosons dynamics is describedby the extended-Bose-Hubbard Hamiltonian on a two-dimensional lattice. Theground state results from the interplay between the lattice geometry and thelong-range interactions, which we account for by means of a classical spinmean-field approach limited by the size of the considered unit cells. Thisextended classical spin mean-field theory accounts for the long-rangedensity-density interaction without truncation. We consider three differentlattice geometries: square, honeycomb, and triangular. In the limit of zerohopping the ground state is always a devil's staircase of solid (gapped)phases. Such crystalline phases with broken translational symmetry are robustwith respect to finite hopping amplitudes. At intermediate hopping amplitudes,these gapped phases melt, giving rise to various lattice supersolid phases,which can have exotic features with multiple sublattice densities. Atsufficiently large hoppings the ground state is a superfluid. The stability ofphases predicted by our approach is gauged by comparison to the known quantumphase diagrams of the Bose-Hubbard model with nearest-neighbour interactions aswell as quantum Monte Carlo simulations for the dipolar case on the squarelattice. Our results are of immediate relevance for experimental realisationsof self-organised crystalline ordering patterns in analogue quantum simulators,e.g., with ultracold dipolar atoms in an optical lattice.

Quantum phases of hardcore bosons with repulsive dipolar density-density interactions on two-dimensional lattices