Entanglement negativity after a local quantum quench in conformal field theories

Xueda Wen, Po-Yao Chang, Shinsei Ryu

Published 2015-01-03Version 1

We study the time evolution of the entanglement negativity after a local quantum quench in conformal field theories (CFTs), where the local quench is introduced by joining two 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 as $\ln t$ at the very beginning of a local quench, where $t$ is the time that elapses after the quench. After developing a plateau-like feature, the entanglement negativity drops to the ground-state value. For the case of two disjoint 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.