https://cea.hal.science/cea-02014494Misguich, GrégoireGrégoireMisguichIPHT - Institut de Physique Théorique - UMR CNRS 3681 - CEA - Commissariat à l'énergie atomique et aux énergies alternatives - Université Paris-Saclay - CNRS - Centre National de la Recherche ScientifiqueMila, FrédéricFrédéricMilaEPFL - Ecole Polytechnique Fédérale de LausanneQuantum dimer model on the triangular lattice: Semiclassical and variational approaches to vison dispersion and condensationHAL CCSD2008[PHYS] Physics [physics]Savelli, Bruno2019-02-11 16:02:482023-03-24 14:53:092019-02-12 11:26:48enJournal articleshttps://cea.hal.science/cea-02014494/document10.1103/physrevb.77.134421application/pdf1After 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.