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Polar Molecules with Three-Body Interactions on the Honeycomb Lattice

We study the phase diagram of ultra-cold bosonic polar molecules loaded on a two-dimensional optical lattice of hexagonal symmetry controlled by external electric and microwave fields. Following a recent proposal in Nature Physics \textbf{3}, 726 (2007), such a system is described by an extended Bose-Hubbard model of hard-core bosons, that includes both extended two- and three-body repulsions. Using quantum Monte-Carlo simulations, exact finite cluster calculations and the tensor network renormalization group, we explore the rich phase diagram of this system, resulting from the strongly competing nature of the three-body repulsions on the honeycomb lattice. Already in the classical limit, they induce complex solid states with large unit cells and macroscopic ground state degeneracies at different fractional lattice fillings. For the quantum regime, we obtain effective descriptions of the various phases in terms of emerging valence bond crystal states and quantum dimer models. Furthermore, we access the experimentally relevant parameter regime, and determine the stability of the crystalline phases towards strong two-body interactions.