Lieb-Robinson bounds and the speed of light from topological order.
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)10.1103/PhysRevB.68.115413]. 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.
Hamma
Alioscia
A
Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5, Canada.
Markopoulou
Fotini
F
Prémont-Schwarz
Isabeau
I
Severini
Simone
S