Lieb-Robinson Bounds and the Speed of Light from Topological Order
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Hamma-2009-Lieb-Robinson Bounds.pdf
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Author(s)
Hamma, Alioscia
Markopoulou, Fotini
Premont-Schwarz, Isabeau
Severini, Simone
Date Issued
January 2009
Journal
Physical Review Letters
Publisher
American Physical Society
Citation
Hamma, Alioscia et al. “Lieb-Robinson Bounds and the Speed of Light from Topological Order.” Physical Review Letters 102.1 (2009): 017204. © 2009 The American Physical Society.
Version
Final published version
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Research Laboratory of Electronics
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DOI of Published Version
http://dx.doi.org/10.1103/PhysRevLett.102.017204
