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Topological Degeneracy and Vortex Manipulation in Kitaev's Honeycomb Model

Kells, G., Bolukbasi, A.T., Lahtinen, V., Slingerland, J.K., Pachos, J.K. and Vala, J. (2008) Topological Degeneracy and Vortex Manipulation in Kitaev's Honeycomb Model. Physical Review Letters, 101 (24). Art. No. 240404. ISSN 1079-7114

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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. We note that these fermions, made from pairs of vortices, can be moved with no additional energy cost.

Item Type: Article
Copyright, Publisher and Additional Information: © 2008 The American Physical Society. This is an author produced version of a paper published in Physical Review Letters. Uploaded in accordance with the publisher's self archiving policy.
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Physics and Astronomy (Leeds)
Depositing User: Sherpa Assistant
Date Deposited: 09 Jan 2009 15:36
Last Modified: 08 Feb 2013 17:05
Published Version: http://dx.doi.org/10.1103/PhysRevLett.101.240404
Status: Published
Publisher: American Physical Society
Refereed: Yes
Identification Number: 10.1103/PhysRevLett.101.240404
URI: http://eprints.whiterose.ac.uk/id/eprint/5318

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