Double-semion topological order from exactly solvable quantum dimer models

TL;DR

This paper constructs exactly solvable quantum dimer models on various 2D lattices that exhibit a fully gapped quantum spin liquid with double-semion topological order, demonstrated through explicit wave function analysis and monomer excitation statistics.

Contribution

It introduces a generalized quantum dimer model with exact ground states showing double-semion topological order on nonbipartite lattices.

Findings

Ground states are fully gapped quantum spin liquids with double-semion order.

Wave functions have nonlocal sign structures based on loop counting.

Monomer excitations exhibit semionic statistics.

Abstract

We construct a generalized quantum dimer model on two-dimensional nonbipartite lattices including the triangular lattice, the star lattice and the kagome lattice. At the Rokhsar-Kivelson (RK) point, we obtain its exact ground states that are shown to be a fully gapped quantum spin liquid with the double-semion topological order. The ground-state wave function of such a model at the RK point is a superposition of dimer configurations with a nonlocal sign structure determined by counting the number of loops in the transition graph. We explicitly demonstrate the double-semion topological order in the ground states by showing the semionic statistics of monomer excitations. We also discuss possible implications of such double-semion resonating valence bond states to candidate quantum spin-liquid systems discovered experimentally and numerically in the past few years.