Z3 topological order in the quantum dimer-pentamer model

2017/04/07 by Owen Myers, C. M. Herdman, Chris M. Herdman · 4 citations
Mathematics · Physics and Astronomy · #Combinatorics #Dimer #Ground state #Hamiltonian (control theory) #Ising model #Mathematics #Pentamer #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Square lattice #Symmetry protected topological order #Topological degeneracy #Topological order #Topology (electrical circuits) #cond-mat.stat-mech

paper · pdf · doi:10.1103/physrevb.96.174434

published in Physical review. B./Physical review. B 96(17) (American Physical Society) · 12 pages, 12 figures

arxiv created 2017/04/07 · openalex publication_date 2017/11/27 · arxiv updated 2017/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We introduce the quantum dimer-pentamer model (QDPM) on the square lattice. This model is a generalization of the square-lattice quantum dimer model as its configuration space comprises fully packed hard-core dimer coverings as well as dimer configurations containing pentamers, where four dimers touch a vertex. Thus in the QDPM, the fully packed, hard-core constraint of the quantum dimer model is relaxed such that the local dimer number at each vertex is fixed modulo 3, resulting in an exact local Z₃ gauge symmetry. We construct a local Hamiltonian for which the Rokhsar-Kivelson (RK) equal superposition state is the exact ground state and has a ninefold topological degeneracy on the torus. Using Monte Carlo calculations, we find no spontaneous symmetry breaking in the RK wave function and that its dimer-dimer correlation function decays exponentially. By doping the QDPM RK state with a pair of monomers, we demonstrate that Z₃ electric charges are deconfined. Additionally, we introduce a Z₃ magnetic string operator that we find decays exponentially and shows no signatures of magnetic vortex condensation. These numerical results suggest that the ground state of the QDPM is a dimer liquid with Z₃ topological order.

Citations

• The statistics of dimers on a lattice
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Effective quantum dimer model for trimerized kagomé antiferromagnet
• Crystallization of the resonating valence bond liquid as vortex condensation
• TOPOLOGICAL ORDERS IN RIGID STATES
• From classical to quantum dynamics at Rokhsar–Kivelson points
• Detecting Topological Order in a Ground State Wave Function
• String-net condensation: A physical mechanism for topological phases
• Classical dimers on the triangular lattice
• Plaquette phase of the square-lattice quantum dimer model: Quantum Monte Carlo calculations
• The cold atom Hubbard toolbox
• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Double-semion topological order from exactly solvable quantum dimer models
• Non-Abelian anyons and topological quantum computation
• Anyonic interferometry and protected memories in atomic spin lattices
• Fractionalization in the Cuprates: Detecting the Topological Order
• On bipartite Rokhsar-Kivelson points and Cantor deconfinement