Topological Defects in Quantum Field Theory with Matrix Product States

• Published in: arXiv.org
• Main Authors: Gillman, Edward, Rajantie, Arttu
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 03.12.2017
• Subjects: Defects; Excitation; Field theory; Ground state; Mathematical analysis; Physics - High Energy Physics - Lattice; Physics - Quantum Physics; Quantum field theory; Quantum theory; Tensors; Topology
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1705.09802

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.