%0 Journal Article %T Quantum dimer model on the triangular lattice: Semiclassical and variational approaches to vison dispersion and condensation %+ Institut de Physique Théorique - UMR CNRS 3681 (IPHT) %+ Ecole Polytechnique Fédérale de Lausanne (EPFL) %A Misguich, Grégoire %A Mila, Frédéric %< avec comité de lecture %@ 1098-0121 %J Physical Review B: Condensed Matter and Materials Physics (1998-2015) %I American Physical Society %V 77 %P 134421 %8 2008-04 %D 2008 %R 10.1103/physrevb.77.134421 %Z PACS numbers: 05.50.q, 71.10.w, 75.10.Jm %Z Physics [physics]Journal articles %X After reviewing the concept of vison excitations in $\mathbb{Z}_2$ 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 $\sqrt{12}$X $\sqrt{12}$ 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. %G English %2 https://cea.hal.science/cea-02014494/document %2 https://cea.hal.science/cea-02014494/file/Misg.pdf %L cea-02014494 %U https://cea.hal.science/cea-02014494 %~ CEA %~ CNRS %~ DSM-IPHT %~ CEA-DRF %~ GS-MATHEMATIQUES %~ GS-PHYSIQUE