Entanglement negativity after a local quantum quench in conformal field theories

TL;DR

This paper investigates how entanglement negativity evolves over time after a local quantum quench in (1+1)-dimensional conformal field theories, revealing growth, plateau, and decay patterns consistent with quasiparticle propagation.

Contribution

It provides explicit analytical calculations of negativity dynamics for both adjacent and disjoint intervals after a local quench in CFTs, supported by numerical verification.

Findings

Negativity grows logarithmically immediately after the quench.

A plateau forms before negativity drops to the ground-state level.

Long-range entanglement can be generated between separated intervals.

Abstract

We study the time evolution of the entanglement negativity after a local quantum quench in (1+1)-dimensional conformal field theories (CFTs), which we introduce by suddenly joining two initially decoupled CFTs at their endpoints. We calculate the negativity evolution for both adjacent intervals and disjoint intervals explicitly. For two adjacent intervals, the entanglement negativity grows logarithmically in time right after the quench. After developing a plateau-like feature, the entanglement negativity drops to the ground-state value. For the case of two spatially separated intervals, a light-cone behavior is observed in the negativity evolution; in addition, a long-range entanglement, which is independent of the distance between two intervals, can be created. Our results agree with the heuristic picture that quasiparticles, which carry entanglement, are emitted from the joining point and propagate freely through the system. Our analytical results are confirmed by numerical calculations based on a critical harmonic chain.