Entanglement growth after inhomogenous quenches

Understand

We study the growth of entanglement in quantum systems with a conserved quantity exhibiting diffusive transport, focusing on how initial inhomogeneities are imprinted on the entropy.

• We propose a simple effective model, which generalizes the minimal cut picture of \textit{Jonay et al.} in such a way that the `line tension' of the cut depends on the local entropy density.
• In the case of noisy dynamics, this is described by a Kardar-Parisi-Zhang (KPZ) equation coupled to a diffusing field.
• We investigate the resulting dynamics and find that initial inhomogeneities of the conserved charge give rise to features in the entanglement profile, whose width and height both grow in time as $\propto\sqrt{t}$.