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 initial state that has short range correlations, measurements of two observers at distant points are expected to remain independent until their past light-cones overlap. This is called the "horizon effect". Surprisingly we find that when topological excitations are present, correlations can develop outside of the horizon, even between infinitely distant points. We demonstrate this effect in the quantum sine-Gordon model, showing that it is completely consistent with relativistic causality and it can be attributed to the non-local nature of soliton and breather excitations.