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Phys. Rev. Lett. 102, 017204 (2009) [4 pages]

Lieb-Robinson Bounds and the Speed of Light from Topological Order

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Alioscia Hamma1,2, Fotini Markopoulou1,2,3, Isabeau Prémont-Schwarz1,2,3, and Simone Severini4
1Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5, Canada
2Massachusetts Institute of Technology, Research Laboratory of Electronics, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
3Department of Physics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
4Institute for Quantum Computing and Department of Combinatorics and Optimization, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada

Received 18 August 2008; revised 29 October 2008; published 5 January 2009

We apply the Lieb-Robinson bounds technique to find the maximum speed of interaction in a spin model with topological order whose low-energy effective theory describes light [see X.-G. Wen Phys. Rev. B 68 115413 (2003)]. The maximum speed of interactions in two dimensions is bounded from above by less than e times the speed of emerging light, giving a strong indication that light is indeed the maximum speed of interactions. This result does not rely on mean field theoretic methods. In higher spatial dimensions, the Lieb-Robinson speed is conjectured to increase linearly with the dimension itself. The implications for the horizon problem in cosmology are discussed.

© 2009 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.102.017204
DOI:
10.1103/PhysRevLett.102.017204
PACS:
75.10.Jm, 05.50.+q, 11.15.−q, 71.10.−w
 
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