Topological degeneracy and vortex manipulation in Kitaev's honeycomb model

Abstract

The classification of loop symmetries in Kitaev's honeycomb lattice model provides a natural framework to study the abelian topological degeneracy. We derive a perturbative low-energy effective Hamiltonian, that is valid to all orders of the expansion and for all possible toroidal configurations. Using this form we demonstrate at what order the system's topological degeneracy is lifted by finite size effects and note that in the thermodynamic limit it is robust to all orders. Further, we demonstrate that the loop symmetries themselves correspond to the creation, propagation and annihilation of fermions. Importantly, we note that these fermions, made from pairs of vortices, can be moved with no additional energy cost.

4 pages, 3 figures, Revised version, accepted to PRL

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• Exact Chiral Spin Liquids and Mean-Field Perturbations of Gamma Matrix Models on the Ruby Lattice
• The Zero Temperature Phase Diagram of the Kitaev Model
• Projective symmetry group classification of $Z_3$ parafermion spin liquids on a honeycomb lattice