Violation of horizon by topological quantum excitations

One of the fundamental principles of relativity is that a physical observable at any space-time point is determined only by events within its past light-cone. In non-equilibrium quantum field theory this is manifested in the way correlations spread through space-time: starting from an initially short-range correlated state, measurements of two observers at distant space-time points are expected to remain independent until their past light-cones overlap, which is usually called the "horizon effect". Surprisingly, we find that in the presence of topological excitations correlations can develop outside of horizon - even between infinitely distant points. We demonstrate this effect in the sine-Gordon model, showing that it can be attributed to the non-local nature of its topological excitations and interpret it as dynamical emergence of entanglement between distant regions of space.