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

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

2008-08-18

arxiv.org/abs/0808.2495v2

Phys.Rev.Lett.102:017204,2009

Physics

Quantum Physics

4 pages, 1 eps figure. Bound improved

Scientific paper

10.1103/PhysRevLett.102.017204

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.

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