Effective Quantum Dimer Model for the Kagome Heisenberg Antiferromagnet: Nearby Quantum Critical Point and Hidden Degeneracy

The low-energy singlet dynamics of the Quantum Heisenberg Antiferromagnet on the Kagome lattice is described by a quantitative Quantum Dimer Model. Using advanced numerical tools, the latter is shown to exhibit Valence Bond Crystal order with a large 36-site unit cell and hidden degeneracy between even and odd parities. Evidences are given that this groundstate lies in the vicinity of a $\mathbb{Z}_2$ dimer liquid region separated by a Quantum Critical Point. Implications regarding numerical analysis and experiments are discussed.