Crystallization of the resonating valence bond liquid as vortex condensation

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)].

arXiv comment4 pages, 4 figures

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• Topological phase transition and single/multi anyon dynamics of $Z_2$ spin liquid
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• Flux roughening in spin ice with mixed $\pm J$ interactions
• Vison condensation and spinon confinement in a kagome-lattice ${\mathbb{Z}}_2$ spin liquid: A numerical study of a quantum dimer model
• Continuous interpolation between the fully frustrated Ising and quantum dimer models
• Symmetrizing the Constraints -- Density Matrix Renormalization Group for Constrained Lattice Models