Entanglement growth after inhomogenous quenches

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 Jonay, Huse, and Nahum [arXiv:1803.00089] 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 the 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 ât. In particular, for a domain wall quench, diffusion restricts entanglement growth to be SvNâ‰t. We find that for charge density wave initial states, these features in the entanglement profile are present even after the charge density has equilibrated. Our conclusions are supported by numerical results on random circuits and deterministic spin chains.