${\mathbb{Z}}_3$ Topological Order in Face Centered Cubic Quantum Plaquette Model

Abstract

We examine the topological order in the resonating singlet valence plaquette (RSVP) phase of the hard-core quantum plaquette model (QPM) on the face centered cubic (FCC) lattice. To do this, we construct a Rohksar-Kivelson type Hamiltonian of local plaquette resonances. This model is shown to exhibit a ${\mathbb{Z}}_3$ topological order, which we show by identifying a ${\mathbb{Z}}_3$ topological constant (which leads to a $3^3$-fold topological ground state degeneracy on the $3$-torus) and topological point-like charge and loop-like magnetic excitations which obey ${\mathbb{Z}}_3$ statistics. We also consider an exactly solvable generalization of this model, which makes the geometrical origin of the ${\mathbb{Z}}_3$ order explicitly clear. For other models and lattices, such generalizations produce a wide variety of topological phases, some of which are novel fracton phases.

12 pages, 6 figures

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• Sorting topological stabilizer models in three dimensions
• Unifying Kitaev magnets, kagome dimer models and ruby Rydberg spin liquids
• Bifurcating entanglement-renormalization group flows of fracton stabilizer models
• Compactifying fracton stabilizer models
• Emergent fermionic gauge theory and foliated fracton order in the Chamon model
• Classification of symmetry-enriched topological quantum spin liquids