Effective quantum dimer model for the kagome Heisenberg antiferromagnet: Nearby quantum critical point and hidden degeneracy

Using an effective Quantum Dimer Model approach, exact diagonalisations of periodic clusters with up to 108 sites (3x6x6) reveal that the Quantum Heisenberg Antiferromagnet on the Kagome lattice lies at a first-order phase transition between two 36-site unit cell Valence Bond Crystals (VBC) preserving lattice point group symmetries but with opposite parities. Evidence for a nearby Quantum Critical Point characterized by the melting of the even VBC into a Z_2 dimer liquid are given. Implications regarding numerical analysis and experiments are discussed.