Topological Degeneracy and Vortex Manipulation in Kitaev’s Honeycomb Model

Kells, G. and Bolukbasi, A.T. and Lahtinen, V. and Slingerland, J.K. and Pachos, J.K. and Vala, J. (2008) Topological Degeneracy and Vortex Manipulation in Kitaev’s Honeycomb Model. Physical Review Letters, 101 (240404). pp. 1-4. ISSN 1079-7114

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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.

Item Type: Article
Additional Information: 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.
Keywords: Topological degeneracy; vortex manipulation; Kitaev honeycomb model; lattice model;
Academic Unit: Faculty of Science and Engineering > Mathematical Physics
Item ID: 2723
Identification Number: DOI: 10.1103/PhysRevLett.101.240404
Depositing User: Dr. Joost Slingerland
Date Deposited: 27 Sep 2011 13:27
Journal or Publication Title: Physical Review Letters
Publisher: American Physical Society
Refereed: Yes

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