Ergodic Archimedean dimers
arXiv:2303.04817 · doi:10.21468/SciPostPhysCore.6.3.054
Abstract
We study perfect matchings, or close-packed dimer coverings, of finite sections of the eleven Archimedean lattices and give a constructive proof showing that any two perfect matchings can be transformed into each other using small sets of local ring-exchange moves. This result has direct consequences for formulating quantum dimer models with a resonating valence bond ground state, i.e., a superposition of all dimer coverings compatible with the boundary conditions. On five of the composite Archimedean lattices we supplement the sufficiency proof with translationally invariant reference configurations that prove the strict necessity of the sufficient terms with respect to ergodicity. We provide examples of and discuss frustration-free deformations of the quantum dimer models on two tripartite lattices.
arXiv commentSubmission to SciPost; 21 pages, 17 figures
References in corpus (33)
- Artificial "spin ice" in a geometrically frustrated lattice of nanoscale ferromagnetic islands
- Probing Topological Spin Liquids on a Programmable Quantum Simulator
- An RVB phase in the triangular lattice quantum dimer model
- Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
- Ultracold Quantum Gases and Lattice Systems: Quantum Simulation of Lattice Gauge Theories
- The Loop Algorithm
- Quantum dimer model on the kagome lattice: solvable dimer liquid and Ising gauge theory
- Quantum phases of Rydberg atoms on a kagome lattice
- Stacked topological insulator built from bismuth-based graphene sheet analogues
- Random Domino Tilings and the Arctic Circle Theorem
- Relaxation time for a dimer covering with height representation
- Classical dimers on the triangular lattice
- Quantum Spin Ice and dimer models with Rydberg atoms
- Emerging 2D Gauge theories in Rydberg configurable arrays
- Dimers on two-dimensional lattices
- An extended Hubbard model with ring exchange: a route to a non-Abelian topological phase
- Quantum phase transition from bounded to extensive entanglement entropy in a frustration-free spin chain
- Hilbert space fragmentation in a 2D quantum spin system with subsystem symmetries
- Deformed Fredkin Spin Chain with Extensive Entanglement
- The plaquette phase of the square lattice quantum dimer model
- Eigenstate thermalization hypothesis in quantum dimer models
- Spangolite: an s=1/2 maple leaf lattice antiferromagnet?
- Two-dimensional lattice gauge theory on a near-term quantum simulator: variational quantum optimization, confinement, and topological order
- Out-of-Time-Ordered Crystals and Fragmentation
- Entropy, gap and a multi-parameter deformation of the Fredkin spin chain
- Classical Dimers on Penrose Tilings
- Partial lifting of degeneracy in the Ising antiferromagnet on the kagome lattice
- Topological RVB quantum spin liquid on the ruby lattice
- The frustration-free fully packed loop model
- Loop condensation in the triangular lattice quantum dimer model
- Coupled Fredkin and Motzkin chains from quantum six- and nineteen-vertex models
- Quantum trimer models and topological SU(3) spin liquids on the kagome lattice
- Classical and quantum dimers on the star lattice