From the SU(2) quantum link model on the honeycomb lattice to the quantum dimer model on the kagome lattice: Phase transition and fractionalized flux strings

We consider the (2+1)-dimensional SU(2) quantum link model on the honeycomb lattice and show that it is equivalent to a quantum dimer model on the kagome lattice. The model has crystalline confined phases with spontaneously broken translation invariance associated with pinwheel order, which is investigated with either a Metropolis or an efficient cluster algorithm. External half-integer non-Abelian charges [which transform nontrivially under the Z(2) center of the SU(2) gauge group] are confined to each other by fractionalized strings with a delocalized Z(2) flux. The strands of the fractionalized flux strings are domain walls that separate distinct pinwheel phases. A second-order phase transition in the three-dimensional Ising universality class separates two confining phases: one with correlated pinwheel orientations, and the other with uncorrelated pinwheel orientations.