Topological excitations in three dimensional Kitaev model

Abstract

We study the excitations in a three dimensional version of Kitaev's spin-1/2 model on the honeycomb lattice introduced by the present authors recently. The gapped phase of the system is analyzed using a low energy effective Hamiltonian which is defined on the diamond lattice and consists of plaquette operators. The excitations of the effective Hamiltonian form loops in an embedded lattice. The elementary excitations, which are the shortest loops, are fermions. Moreover, the excitations obey nontrivial braiding rules: when a fermion winds through a loop, the wave function acquires a phase $\pi$.

6 pages, 4 figures

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• Recent progress on correlated electron systems with strong spin-orbit coupling
• Designing Kitaev spin liquids in metal-organic frameworks
• Fractional Chiral Hinge Insulator
• Entanglement and Majorana edge states in the Kitaev model
• Chiral Spin Liquids at Finite Temperature in a Three-Dimensional Kitaev Model
• Topological entanglement entropy of three-dimensional Kitaev model
• Defect production and quench dynamics in the three-dimensional Kitaev model
• A primer on Kitaev Model: Basic aspects, material realization, and recent experiments
• Global constraints on $Z_2$ fluxes in two different anisotropic limits of a hypernonagon Kitaev model
• Deciphering competing interactions of Kitaev-Heisenberg-$\Gamma$ system in clusters: part II -- dynamics of Majorana fermions