The Kibble Zurek mechanism in a relativistic ${\varphi }^4$ scalar field theory in $D=(1+1)$ is studied using uniform matrix product states. The equal time two point function in momentum space $G_2(k)$ is approximated as the system is driven through a quantum phase transition at a variety of different quench rates ${\tau }_Q$. We focus on looking for signatures of topological defect formation in the system and demonstrate the consistency of the picture that the two point function $G_2(k)$ displays two characteristic scales, the defect density $n$ and the kink width $d_K$. Consequently, $G_2(k)$ provides a clear signature for the formation of defects and a well defined measure of the defect density in the system. These results provide a benchmark for the use of tensor networks as powerful nonperturbative nonequilibrium methods for relativistic quantum field theory, providing a promising technique for the future study of high energy physics and cosmology.

• Received 14 January 2018

DOI:https://doi.org/10.1103/PhysRevD.97.094505