Entanglement Negativity and Mutual Information after a Quantum Quench: Exact Link from Space-Time Duality

Bertini, Bruno; Klobas, Katja; Lu, Tsung-Cheng

Abstract

We study the growth of entanglement between two adjacent regions in a tripartite, one-dimensional many-body system after a quantum quench. Combining a replica trick with a space-time duality transformation, we derive an exact, universal relation between the entanglement negativity and Rényi-1/2 mutual information that holds at times shorter than the sizes of all subsystems. Our proof is directly applicable to any local quantum circuit, i.e., any lattice system in discrete time characterized by local interactions, irrespective of the nature of its dynamics. Our derivation indicates that such a relation can be directly extended to any system where information spreads with a finite maximal velocity.

Citation

Bertini, B., Klobas, K., & Lu, T.-C. (2022). Entanglement Negativity and Mutual Information after a Quantum Quench: Exact Link from Space-Time Duality. Physical Review Letters, 129(14), Article 140503. https://doi.org/10.1103/physrevlett.129.140503

• Journal Article Type: Article
• Acceptance Date: Sep 7, 2022
• Online Publication Date: Sep 30, 2022
• Publication Date: Sep 30, 2022
• Deposit Date: Nov 9, 2022
• Publicly Available Date: Nov 15, 2022
• Journal: Physical Review Letters
• Print ISSN: 0031-9007
• Electronic ISSN: 1079-7114
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 129
• Issue: 14
• Article Number: 140503
• DOI: https://doi.org/10.1103/physrevlett.129.140503
• Keywords: General Physics and Astronomy
• Public URL: https://nottingham-repository.worktribe.com/output/13166363
• Publisher URL: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.140503