Quantum Dimer Model on the Kagome Lattice: Solvable Dimer-Liquid and Ising Gauge Theory

TLDR

Corner‑sharing‑triangle lattices, such as the kagome lattice, can be defined in arbitrary geometry. The authors introduce quantum dimer models on these lattices to provide a simple framework for studying fractionalization, topological order, and their relation to Z₂ gauge theories. They construct the models by defining quantum dimer configurations on corner‑sharing‑triangle lattices. The models exhibit a fully disordered, gapped dimer‑liquid phase with topological degeneracy and deconfined fractional excitations, as well as solid phases, and allow exact determination of the full dimer‑liquid spectrum.

Abstract

We introduce quantum dimer models on lattices made of corner-sharing triangles. These lattices include the kagome lattice and can be defined in arbitrary geometry. They realize fully disordered and gapped dimer-liquid phase with topological degeneracy and deconfined fractional excitations, as well as solid phases. Using geometrical properties of the lattice, several results are obtained exactly, including the full spectrum of a dimer liquid. These models offer a very natural--and maybe the simplest possible--framework to illustrate general concepts such as fractionalization, topological order, and relation to ${\mathbb{Z}}_{2}$ gauge theories.