The Kibble Zurek Mechanism of Topological Defect Formation in Quantum Field Theory with Matrix Product States

Abstract

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 non-perturbative non-equilibrium methods for relativistic quantum field theory, providing a promising technique for the future study of high energy physics and cosmology.

18 pages, 8 figures : v3 ; version accepted for publication in PRD

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