# Out-of-horizon correlations following a quench in a relativistic quantum field theory

## TL;DR

This paper investigates how topological excitations in a relativistic quantum field theory can lead to correlations developing outside the expected light-cone horizon after a quench, challenging the conventional horizon effect.

## Contribution

It demonstrates that topological excitations cause correlations to appear beyond the light-cone in the sine-Gordon model, revealing new non-equilibrium phenomena.

## Key findings

- Correlations can develop outside the horizon due to topological effects.
- Initial clustering of correlations is necessary for the horizon effect.
- Sine-Gordon quenches violate clustering for soliton fields, affecting local correlations.

## Abstract

One of the manifestations of relativistic invariance in non-equilibrium quantum field theory is the "horizon effect" a.k.a. light-cone spreading of correlations: 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. Surprisingly, we find that in the presence of topological excitations correlations can develop outside of horizon and indeed even between infinitely distant points. We demonstrate this effect for a wide class of global quantum quenches to the sine-Gordon model. We point out that besides the maximum velocity bound implied by relativistic invariance, clustering of initial correlations is required to establish the "horizon effect". We show that quenches in the sine-Gordon model have an interesting property: despite the fact that the initial states have exponentially decaying correlations and cluster in terms of the bosonic fields, they violate the clustering condition for the soliton fields, which is argued to be related to the non-trivial field topology. The nonlinear dynamics governed by the solitons makes the clustering violation manifest also in correlations of the local bosonic fields after the quench.