Critical slowing down and entanglement protection

We consider a quantum device D interacting with a quantum many-body environment R which features a second-order phase transition at T = 0. Exploiting the description of the critical slowing down undergone by R according to the Kibble-Zurek mechanism, we explore the possibility to freeze the environment in a configuration such that its impact on the device is significantly reduced. Within this framework, we focus on the magnetic-domain formation typical of the critical behavior in spin models and propose a strategy that allows one to protect the entanglement between different components of D from the detrimental effects of the environment.