Kitaev model and dimer coverings on the honeycomb lattice

Abstract

We consider an extension of the Kitaev honeycomb model based on arbitrary dimer coverings satisfying matching rules. We focus on three different dimer coverings having the smallest unit cells for which we calculate the ground-state phase diagram. We also study one- and two-vortex properties for these coverings in the Abelian phases and show that vortex-vortex interactions can be attractive or repulsive. These qualitative differences are confirmed analytically by high-order perturbative expansions around the isolated-dimer limit. Similarities and differences with the original Kitaev honeycomb model are discussed.

8 pages, 9 figures, published version

References in corpus (12)

• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Kitaev-Heisenberg Model on Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides $A_2$IrO${}_3$
• An exact chiral spin liquid with non-Abelian anyons
• Disorder in a quantum spin liquid: flux binding and local moment formation
• Anyonic interferometry and protected memories in atomic spin lattices
• Collective States of Interacting Anyons, Edge States, and the Nucleation of Topological Liquids
• Emergent Fermions and Anyons in the Kitaev Model
• Perturbative approach to an exactly solved problem: the Kitaev honeycomb model
• Creation and Manipulation of Anyons in the Kitaev Model
• Perturbative study of the Kitaev model with spontaneous time-reversal symmetry breaking
• Topological phase transitions driven by gauge fields in an exactly solvable model
• The Zero Temperature Phase Diagram of the Kitaev Model

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