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Brennan, John and Vala, Jiri (2018) The Kitaev honeycomb model on surfaces of genus g ≥ 2. New Journal of Physics (NJP), 20 (053023). ISSN 1367-2630
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Abstract
We present a construction of the Kitaev honeycomb lattice model on an arbitrary higher genus surface. We first generalize the exact solution of the model based on the Jordan–Wigner fermionization to a surface with genus g = 2, and then use this as a basic module to extend the solution to lattices of arbitrary genus. We demonstrate our method by calculating the ground states of the model in both the Abelian doubled phase and the non-Abelian Ising topological phase on lattices with the genus up to g = 6. We verify the expected ground state degeneracy of the system in both topological phases and further illuminate the role of fermionic parity in the Abelian phase.
| Item Type: | Article |
|---|---|
| Additional Information: | Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Cite as: John Brennan and Jiří Vala 2018 New J. Phys. 20 053023 |
| Keywords: | topological phase; topological quantum field theory; topological degeneracy; lattice defect; |
| Academic Unit: | Faculty of Science and Engineering > Theoretical Physics |
| Item ID: | 13149 |
| Identification Number: | 10.1088/1367-2630/aabb95 |
| Depositing User: | Dr. Jiri Vala |
| Date Deposited: | 31 Jul 2020 15:31 |
| Journal or Publication Title: | New Journal of Physics (NJP) |
| Publisher: | Institute of Physics (IoP) and Deutsche Physikalische Gesellschaft |
| Refereed: | Yes |
| Related URLs: | |
| URI: | https://mural.maynoothuniversity.ie/id/eprint/13149 |
| Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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