Parity of Chern numbers in the Kitaev honeycomb model and the sixteenfold way

Abstract

In two dimensions, topological phases of free Majorana fermions coupled to a ${\mathbb{Z}}_2$ gauge field are known to be classified according to the Chern number $\nu \in \mathbb{Z}$. Its value mod 16 specifies the type of anyonic excitations. In this paper, we investigate triangular vortex configurations (and their dual) in the Kitaev honeycomb model and show that fourteen of these sixteen phases can be obtained by adding a time-reversal symmetry-breaking term. Missing phases are $\nu =\pm 7$. More generally, we prove that any periodic vortex configuration with an odd number of vortices per geometric unit cell can only host even Chern numbers whereas odd Chern numbers can be found in other cases.

15 pages, 21 figures, minor typos corrected

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• Magnetic-field Induced Topological Transitions and Thermal Conductivity in a Generalized Kitaev Model
• Kitaev model on Hurwitz hyperbolic tilings: A non-Abelian gapped chiral spin liquid
• Anyon condensation and confinement transition in a Kitaev spin liquid bilayer
• Chiral conformal field theory for topological states and the anyon eigenbasis on the torus
• Lacing topological orders in two dimensions: exactly solvable models for Kitaev's sixteen-fold way
• Effective models for dense vortex lattices in the Kitaev honeycomb model
• Majorana Gap Formation in the Anisotropic Kitaev Model with Ordered Flux Configuration
• Disorder, Low-Energy Excitations, and Topology in the Kitaev Spin Liquid
• Tuning the Chern number of Kitaev quantum spin liquid
• Fractional Wannier Orbitals and Tight-Binding Gauge Fields for Kitaev Honeycomb Superlattices with Flat Majorana Bands