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

TL;DR

This paper uses matrix product states to study the Kibble Zurek mechanism in a relativistic quantum field theory, identifying defect signatures and providing a non-perturbative approach for non-equilibrium phenomena.

Contribution

It demonstrates the effectiveness of tensor network methods in analyzing topological defect formation during quantum phase transitions in relativistic field theories.

Findings

G_{2}(k) shows two characteristic scales: defect density and kink width

G_{2}(k) signatures correlate with defect formation

Tensor networks serve as a promising non-perturbative tool for quantum field theory

Abstract

The Kibble Zurek mechanism in a relativistic $\phi^{4}$ 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.