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

Abstract : 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.
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Grégoire Misguich, Frédéric Mila. Quantum dimer model on the triangular lattice: Semiclassical and variational approaches to vison dispersion and condensation. Physical Review B : Condensed matter and materials physics, American Physical Society, 2008, 77, pp.134421. ⟨10.1103/physrevb.77.134421⟩. ⟨cea-02014494⟩

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