# Topological Defects in Quantum Field Theory with Matrix Product States

## TL;DR

This paper demonstrates how matrix product states can effectively model topological defects in a relativistic scalar field theory, enabling calculation of kink properties and insights into defect dynamics.

## Contribution

It introduces a general tensor network approach to study topological defects in quantum field theories, including methods to compute kink mass and analyze defect-antikink contributions.

## Key findings

- Successfully approximated kink states as matrix product states
- Calculated kink mass and compared it with theoretical expectations
- Showed the method's applicability to non-equilibrium defect physics

## Abstract

Topological defects (kinks) in a relativistic $\phi^{4}$ scalar field theory in $D=(1+1)$ are studied using the matrix product state tensor network. The one kink state is approximated as a matrix product state and the kink mass is calculated. The approach used is quite general and can be applied to a variety of theories and tensor networks. Additionally, the contribution of kink-antikink excitations to the ground state is examined and a general method to estimate the scalar mass from equal time ground state observables is provided. The scalar and kink mass are compared at strong coupling and behave as expected from universality arguments. This suggests that the matrix product state can adequately capture the physics of defect-antidefect excitations and thus provides a promising technique to study challenging non-equilibrium physics such as the Kibble-Zurek mechanism of defect formation.