Lieb-Robinson bounds and the speed of light from topological order

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, \prb {\bf 68}, 115413 (2003)]. The maximum speed of interactions is found in two dimensions is bounded from above less than $\sqrt{2}e$ 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. Implications for the horizon problem in cosmology are discussed.

4 pages, 1 eps figure. Bound improved

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• Lieb-Robinson bounds and the generation of correlations and topological quantum order
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• Propagation of Correlations in Quantum Lattice Systems
• General entanglement scaling laws from time evolution
• Quantum Graphity: a model of emergent locality

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