Topological degeneracy and vortex manipulation in Kitaev's honeycomb model

Details Topological degeneracy and vortex manipulation in Kitaev's honeycomb model Topological degeneracy and vortex manipulation in Kitaev's honeycomb model

2008-04-17

arxiv.org/abs/0804.2753v3

Phys.Rev.Lett.101:240404,2008

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

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

Scientific paper

10.1103/PhysRevLett.101.240404

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.

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