Valence Bond Solids and Their Quantum Melting in Hard-Core Bosons on the   Kagome Lattice
  Using large scale quantum Monte Carlo simulations and dual vortex theory we analyze the ground state phase diagram of hard-core bosons on the kagome lattice with nearest neighbor repulsion. In contrast to the case of a triangular lattice, no supersolid emerges for strong interactions. While a uniform superfluid prevails at half-filling, two novel solid phases emerge at densities $\rho=1/3$ and $\rho=2/3$. These solids exhibit an only partial ordering of the bosonic density, allowing for local resonances on a subset of hexagons of the kagome lattice. We provide evidence for a weakly first-order phase transition at the quantum melting point between these solid phases and the superfluid. 
S. V. Isakov, S. Wessel, R. G. Melko, K. Sengupta, Yong Baek Kim