Quantum dimer model with extensive ground-state entropy on the kagome lattice

We introduce a quantum dimer model on the kagome lattice with kinetic terms allowing from three to six dimers to resonate around hexagons. Unlike the models studied previously, the different resonance loops appear with different signs (given by the parity of the number of dimers involved). These signs naturally appear when performing the lowest-order overlap expansion (Rokhsar and Kivelson 1988) of the Heisenberg model. We demonstrate that the quantum dimer model has an extensive zero-temperature entropy and has very short-range dimer-dimer correlations. We discuss the possible relevance of this kind of quantum dimer liquid to the physics of the spin-$\frac{1}{2}$ Heisenberg model on the kagome lattice.