Kells, G. and Bolukbasi, A.T. and Lahtinen, V. and Slingerland, J.K. and Pachos, J.K. and Vala, J.
Topological Degeneracy and Vortex Manipulation in Kitaev’s Honeycomb Model.
Physical Review Letters, 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. We
note that these fermions, made from pairs of vortices, can be moved with no additional energy cost.
||Original article published in Physical Review Letters Vol.101 No.240404(2008) © 2008 The American Physical Society. We acknowledge the support of SFI through the PIYRA
and of EU networks EMALI, SCALA, EPSRC, the Royal
Society, the Finnish Academy of Science, and ICHEC. We
thank Gregoire Misguich and Simon Trebst for discussions
and Timothy Stitt and Niall Moran for assistance in the
early stages of this work.
||Topological degeneracy; vortex manipulation; Kitaev honeycomb model; lattice model;
||Faculty of Science and Engineering > Mathematical Physics
Dr. Joost Slingerland
||27 Sep 2011 13:27
|Journal or Publication Title:
||Physical Review Letters
||American Physical Society
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