Crystallization of the resonating valence bond liquid as vortex condensation

TL;DR

This paper demonstrates that the liquid-to-crystal transition in a quantum dimer model on a triangular lattice occurs via vortex (vison) condensation, with numerical evidence showing visons as the lowest excitations whose gap closes at the transition.

Contribution

It provides numerical evidence that vison condensation drives the phase transition in the Rokhsar--Kivelson dimer model, confirming theoretical predictions about the nature of the transition.

Findings

Visons are the lowest excitations in the liquid phase.

Vison gap decreases continuously to zero at the transition.

The transition is second order, consistent with prior theories.

Abstract

We show that the liquid-to-crystal quantum phase transition in the Rokhsar--Kivelson dimer model on the two-dimensional triangular lattice occurs as a condensation of vortex-like excitations called ``visons''. This conclusion is drawn from the numerical studies of the vison spectrum in the liquid phase by using the Green's function Monte Carlo method. We find that visons remain the lowest excitation throughout the liquid phase and that their gap decreases continuously to zero at the phase transition. The nature of the crystal phase and the second order of the phase transition are in agreement with the earlier prediction of Moessner and Sondhi [Phys. Rev. B 63, 224401 (2001)].