Toward Kitaev's sixteenfold way in a honeycomb lattice model

Abstract

Kitaev's sixteenfold way is a classification of exotic topological orders in which ${\mathbb{Z}}_2$ gauge theory is coupled to Majorana fermions of Chern number $C$. The $16$ distinct topological orders within this class, depending on $C\mathrm{mod}16$, possess a rich variety of Abelian and non-Abelian anyons. We realize more than half of Kitaev's sixteenfold way, corresponding to Chern numbers $0$, $\pm 1$, $\pm 2$, $\pm 3$, $\pm 4$, and $\pm 8$, in an exactly solvable generalization of the Kitaev honeycomb model. For each topological order, we explicitly identify the anyonic excitations and confirm their topological properties. In doing so, we observe that the interplay between lattice symmetry and anyon permutation symmetry may lead to a "weak supersymmetry" in the anyon spectrum. The topological orders in our honeycomb lattice model could be directly relevant for honeycomb Kitaev materials, such as $\alpha$-RuCl${}_3$, and would be distinguishable by their specific quantized values of the thermal Hall conductivity.

arXiv comment13 pages, 11 figures

References in corpus (39)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Anyons in an exactly solved model and beyond
• Topological entanglement entropy
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Detecting topological order in a ground state wave function
• Kitaev-Heisenberg Model on Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides $A_2$IrO${}_3$
• Quantum Orders and Symmetric Spin Liquids
• Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• $\alpha$-RuCl3: a Spin-Orbit Assisted Mott Insulator on a Honeycomb Lattice
• Relevance of the Heisenberg-Kitaev model for the honeycomb lattice iridates A_2IrO_3
• Neutron tomography of magnetic Majorana fermions in a proximate quantum spin liquid
• Spin waves and revised crystal structure of honeycomb iridate Na2IrO3
• The monoclinic crystal structure of $\alpha$-RuCl${}_3$ and the zigzag antiferromagnetic ground state
• Scattering Continuum and Possible Fractionalized Excitations in $\alpha$-RuCl${}_3$
• Magnetic order in $\alpha$-RuCl${}_3$: a honeycomb lattice quantum magnet with strong spin-orbit coupling
• Direct evidence of a zigzag spin chain structure in the honeycomb lattice: A neutron and x-ray diffraction investigation on single crystal $\mathrm{N}{\mathrm{a}}_2\mathrm{Ir}{\mathrm{O}}_3$
• The Flux-Phase of the Half-Filled Band
• Long range magnetic ordering in Na${}_2$IrO${}_3$
• Pseudospin exchange interactions in d^7 cobalt compounds: Possible realization of the Kitaev model
• Na2IrO3 as a spin-orbit-assisted antiferromagnetic insulator with a 340 meV gap
• Kitaev-Heisenberg Hamiltonian for High-Spin $d^7$ Mott Insulators
• Anisotropic Ru3+ 4d5 magnetism in the alpha-RuCl3 honeycomb system: susceptibility, specific heat and Zero field NMR
• Incommensurate Counterrotating Magnetic Order Stabilized by Kitaev Interactions in the Layered Honeycomb $\alpha$-Li${}_2$IrO${}_3$
• Doping a spin-orbit Mott Insulator: Topological Superconductivity from the Kitaev-Heisenberg Model and possible application to (Na2/Li2)IrO3
• Spin-orbit excitations and electronic structure of the putative Kitaev magnet $\alpha$-RuCl${}_3$
• One Proximate Kitaev Spin Liquid in the $K$-$J$-$\Gamma$ Model on the Honeycomb Lattice
• Magnetic order in single crystals of Na3Co2SbO6 with a honeycomb arrangement of 3d${}^7$ Co${}^{2+}$ ions
• All Majorana Models with Translation Symmetry are Supersymmetric
• Distant-Neighbor Hopping in Graphene and Haldane Models
• Antiferromagnetic Kitaev Interaction in $f$-Electron Based Honeycomb Magnets
• Kitaev materials beyond iridates: order by quantum disorder and Weyl magnons in rare-earth double perovskites
• Topological liquid nucleation induced by vortex-vortex interactions in Kitaev's honeycomb model
• Spin-Peierls Instability of Three-Dimensional Spin Liquids with Majorana Fermi Surfaces
• Crystal field splitting, local anisotropy, and low energy excitations in the quantum magnet YbCl${}_3$
• Vison Crystals in an Extended Kitaev Model on the Honeycomb Lattice
• Kaleidoscope of topological phases with multiple Majorana species
• Topological phase transitions driven by gauge fields in an exactly solvable model

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• Parity of Chern numbers in the Kitaev honeycomb model and the sixteenfold way
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• Magnetoelectric generation of a Majorana-Fermi surface in Kitaev's honeycomb model
• Majorana correlations in the Kitaev model with ordered-flux structures
• Symmetry-protected gapless spin liquids on the strained honeycomb lattice
• Topological Nematic Phase Transition in Kitaev Magnets Under Applied Magnetic Fields
• Magnetic-field Induced Topological Transitions and Thermal Conductivity in a Generalized Kitaev Model
• Anyon condensation and confinement transition in a Kitaev spin liquid bilayer
• Multinode quantum spin liquids in extended Kitaev honeycomb models: the view from variational Monte Carlo
• Multipolar spin liquid in an exactly solvable model for $j_{\mathrm{eff}}=\frac{3}{2}$ moments
• Effective models for dense vortex lattices in the Kitaev honeycomb model
• Lacing topological orders in two dimensions: exactly solvable models for Kitaev's sixteen-fold way
• Majorana Gap Formation in the Anisotropic Kitaev Model with Ordered Flux Configuration
• The Kekulé-Kitaev model: linear and non-linear responses and magnetic field effects
• Fractional Wannier Orbitals and Tight-Binding Gauge Fields for Kitaev Honeycomb Superlattices with Flat Majorana Bands
• Tuning the Chern number of Kitaev quantum spin liquid