From the $SU(2)$ Quantum Link Model on the Honeycomb Lattice to the Quantum Dimer Model on the Kagom\'e Lattice: Phase Transition and Fractionalized Flux Strings

TL;DR

This paper maps an $SU(2)$ quantum link model on the honeycomb lattice to a quantum dimer model on the Kagomé lattice, revealing phase transitions, fractionalized flux strings, and pinwheel order with implications for confinement and topological phases.

Contribution

It establishes an exact equivalence between the $SU(2)$ quantum link model and the quantum dimer model on the Kagomé lattice, and analyzes the phase structure and fractionalized flux strings.

Findings

Identifies a second-order phase transition in the 3D Ising universality class.

Discovers fractionalized flux strings connecting external charges.

Characterizes crystalline confined phases with pinwheel order.

Abstract

We consider the $(2+1)$-d $SU(2)$ quantum link model on the honeycomb lattice and show that it is equivalent to a quantum dimer model on the Kagom\'e 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 non-trivially under the $\mathbb{Z}(2)$ center of the $SU(2)$ gauge group) are confined to each other by fractionalized strings with a delocalized $\mathbb{Z}(2)$ flux. The strands of the fractionalized flux strings are domain walls that separate distinct pinwheel phases. A second-order phase transition in the 3-d Ising universality class separates two confining phases; one with correlated pinwheel orientations, and the other with uncorrelated pinwheel orientations.