Abstract
The Kibble Zurek mechanism in a relativistic φ⁴ scalar field theory in D = (1 + 1) is studied using uniform matrix product states. The equal time two point function in momentum space G₂(k) is approximated as the system is driven through a quantum phase transition at a variety of different quench rates τ_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 G₂(k) displays two characteristic scales, the defect density n and the kink width d_K. Consequently, G₂(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.