Abstract
We present results form quantum Monte Carlo simulations of ultra-cold bosonic atoms on frustrated optical lattices such as the triangular and the kagome lattice. For the triangular lattice case a supersolid state of matter emerges, resulting from a novel order-by-disorder effect in the quantum regime. On the kagome lattice no supersolid appears, instead the atoms form exotic valence-bond-solids with local bosonic resonances. The quantum melting of these solids into the superfluid takes place at weakly first-order quantum phase transitions. Relevant algorithmic improvements which allow for large-scale simulations of such systems are mentioned as well as possible experimental realizations of these scenarios based on current experimental advances in quantum optics.
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