Ballistic entanglement cloud after a boundary quench

Entanglement has been extensively used to characterize the structure of strongly correlated many-body systems. Most of these analyses focus on either spatial properties of entanglement or its temporal behavior. Negativity, as an entanglement measure, quantifies entanglement between different noncomplementary blocks of a many-body system. Here, we consider a combined spatial-temporal analysis of entanglement negativity in a strongly correlated many-body system to characterize complex formation of correlations through nonequilibrium dynamics of such systems. A bond defect is introduced through a local quench at one of the boundaries of a uniform Heisenberg spin chain. Using negativity and entanglement entropy, computed by the time-dependent density-matrix renormalization group, we analyze the extension of entanglement in the model as a function of time. We find that an entanglement cloud is formed, detached from the boundary spin and composed of spins with which it is highly entangled. The cloud travels ballistically in the chain until it reaches the other end where it reflects back and the cycle repeats. The revival dynamics exhibits an intriguing contraction (expansion) of the cloud as it moves away from (towards) the boundary spin.