Competing valence bond crystals in the kagome quantum dimer model

The singlet dynamics, which plays a major role in the physics of the spin-1/2 quantum Heisenberg antiferromagnet (QHAF) on the kagome lattice, can be approximately described by projecting onto the nearest-neighbor valence bond (NNVB) singlet subspace. We revisit here the effective quantum dimer model, which originates from the latter NNVB-projected Heisenberg model via a nonperturbative Rokhsar-Kivelson-like scheme. By using Lanczos exact diagonalization on a 108-site cluster supplemented by a careful symmetry analysis, it is shown that a previously found 36-site valence bond crystal (VBC) in fact competes with a new type of 12-site ``resonating-columnar'' VBC. Interestingly, these two VBCs ``emerge'' in different topological sectors. The exceptionally large degeneracy of the ground-state multiplets (144 on our 108-site cluster) and the proximity of a Z₂ dimer liquid have implications for the interpretation of numerical results on the QHAF, which are outlined. The possibility of a chiral VBC (i.e., spontaneously breaking time-reversal symmetry) is also discussed.