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 (VBC) order with a large 36-site unit cell and hidden degeneracy between even odd parities. Evidences are given that this ground state lies in the vicinity of a Z(2) dimer-liquid region separated by a quantum critical point (QCP). Implications regarding numerical analysis and experiments are discussed.