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

TL;DR

This paper uses Lieb-Robinson bounds to demonstrate that the maximum speed of interactions in a topologically ordered spin model in two dimensions is less than a factor of rom the speed of light, suggesting light is the ultimate speed limit.

Contribution

It applies Lieb-Robinson bounds to topologically ordered systems to estimate the maximum interaction speed, providing a non-mean-field proof that aligns with the speed of light.

Findings

Maximum interaction speed in 2D is less than rom light speed.

Speed conjectured to increase linearly with spatial dimension.

Implications discussed for cosmological horizon problem.

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.