Quantum dimer model on the kagome lattice: solvable dimer liquid and Ising gauge theory

TL;DR

This paper introduces quantum dimer models on corner-sharing triangle lattices like kagome, revealing exactly solvable dimer liquids with topological order, fractional excitations, and connections to Z_2 gauge theories.

Contribution

It presents a new class of exactly solvable quantum dimer models on kagome and similar lattices, illustrating topological order and fractionalization.

Findings

Exact spectrum of the dimer-liquid phase obtained

Models exhibit topological degeneracy and fractional excitations

Framework connects dimer models to Z_2 gauge theories

Abstract

We introduce quantum dimer models on lattices made of corner-sharing triangles. These lattices includes 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 Z_2 gauge theories.