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

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 Renyi1/2 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.

Automated summary

In this study, the growth of entanglement between adjacent regions in a one-dimensional many-body system was investigated after a quantum quench. By using a replica trick and a space-time duality transformation, an exact and universal relationship between entanglement negativity and Renyi1/2 mutual information was derived, which holds for times shorter than the sizes of all subsystems. The result suggests that this relationship can be extended to any system where information spreads with a finite maximal velocity.