Double-semion topological order from exactly solvable quantum dimer models

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.

12pages, 10 figures; added the journal references

References in corpus (11)

• Non-Abelian Anyons and Topological Quantum Computation
• Identifying Topological Order by Entanglement Entropy
• An exact chiral spin liquid with non-Abelian anyons
• Chiral spin liquid and emergent anyons in a Kagome lattice Mott insulator
• Emergent Chiral Spin Liquid: Fractional Quantum Hall Effect in a Kagome Heisenberg Model
• Chiral spin liquid in a frustrated anisotropic kagome Heisenberg model
• Resonating valence bond states in the PEPS formalism
• Distinct Spin Liquids and their Transitions in Spin-1/2 XXZ Kagome Antiferromagnets
• Constraints on topological order in Mott Insulators
• Double Semion Phase in an Exactly Solvable Quantum Dimer Model on the Kagome Lattice
• Semionic resonating valence bond states

Cited by in corpus (15)

• Diagnosing phases of magnetic insulators via noise magnetometry with spin qubits
• Quantum Error Correction with the Semion Code
• Unifying Kitaev magnets, kagome dimer models and ruby Rydberg spin liquids
• Ising Anyons in Frustration-Free Majorana-Dimer Models
• Evidence for deconfined $U(1)$ gauge theory at the transition between toric code and double semion
• Dyonic Lieb-Shultz-Mattis Theorem and Symmetry Protected Topological Phases in Decorated Dimer Models
• Emergent spin-1 trimerized valence bond crystal in the spin-1/2 Heisenberg model on the star lattice
• Spin-one bilinear-biquadratic model on a star lattice
• A gapped SU(3) spin liquid with Z_3 topological order
• Re-entrance effect in the high-temperature critical phase of the quantum dimer model on the square lattice
• $Z_3$ topological order in the quantum dimer-pentamer model
• Models of interacting bosons with exact ground states: a unified approach
• The ${\mathbb{Z}}_2$ toric-code and the double-semion topological order of hardcore Bose-Hubbard-type models in the strong-interaction limit
• Multistage spin correlations in the $s$ = 1/2 stuffed hyper-star lattice Li${}_2$Cu${}_2$(MoO${}_4$)${}_3$
• Exactly Solvable Topological Phase Transition in a Quantum Dimer Model