Quantum Darwinism and non-Markovian dissipative dynamics from quantum phases of the spin-1/2 XX model

Quantum Darwinism explains the emergence of a classical description of objects in terms of the creation of many redundant registers in an environment containing their classical information. This amplification phenomenon, where only classical information reaches the macroscopic observer and through which different observers can agree on the objective existence of such object, has been revived lately for several types of situations, successfully explaining classicality. We explore quantum Darwinism in the setting of an environment made of two level systems which are initially prepared in the ground state of the XX model, which exhibits different phases; we find that the different phases have different ability to redundantly acquire classical information about the system, being the "ferromagnetic phase" the only one able to complete quantum Darwinism. At the same time we relate this ability to how non-Markovian the system dynamics is, based on the interpretation that non-Markovian dynamics is associated to back flow of information from environment to system, thus spoiling the information transfer needed for Darwinism. Finally, we explore mixing of bath registers by allowing a small interaction among them, finding that this spoils the stored information as previously found in the literature.