Quantum dimer model on the triangular lattice: Semiclassical and variational approaches to vison dispersion and condensation

After reviewing the concept of vison excitations in Z(2) dimer liquids, we study the liquid-crystal transition of the quantum dimer model on the triangular lattice by means of a semiclassical spin-wave approximation to the dispersion of visons in the context of a "soft-dimer" version of the model. This approach captures some important qualitative features of the transition: continuous nature of the transition, linear dispersion at the critical point, and root 12 x root 12 symmetry-breaking pattern. In a second part, we present a variational calculation of the vison dispersion relation at the Rokhsar-Kivelson (RK) point, which reproduces the qualitative shape of the dispersion relation and the order of magnitude of the gap. This approach provides a simple but reliable approximation of the vison wave functions at the RK point.