Quantum Dimer Model on the triangular lattice: Semiclassical and variational approaches to vison dispersion and condensation

TL;DR

This paper investigates vison excitations in the Quantum Dimer Model on a triangular lattice using semiclassical and variational methods, revealing insights into the liquid-crystal transition and vison dispersion characteristics.

Contribution

It introduces semiclassical spin-wave and variational approaches to analyze vison dispersion and the phase transition in the Quantum Dimer Model on the triangular lattice.

Findings

Captured the continuous nature of the transition

Identified linear dispersion at the critical point

Reproduced the shape and magnitude of the vison gap

Abstract

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 \sqrt{12}x\sqrt{12} symmetry-breaking pattern. In a second part, we present a variational calculation of the vison dispersion relation at the 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.