Non-equilibrium quantum matter through the prism of quantum entanglement

The remarkable experimental advances made it possible to create highly tunable quantum systems of ultracold atoms and trapped ions. These platforms proved to be uniquely suited for probing non-equilibrium behavior of interacting quantum systems. From statistical mechanics, we expect that a non-equilibrium system will thermalize, settling to a state of thermodynamic equilibrium. Surprisingly, there are classes of systems which do not follow this expectation. I will give examples of systems which avoid thermalization, thanks to disorder-induced localization and quantum scarring. While thermalization leads to “scrambling” of quantum information, its absence may protect local quantum coherence. This enables non-equilibrium states of matter not envisioned within the framework of statistical mechanics. I will highlight the recent theoretical insights into the remarkable physical properties of such states, based on the underlying patterns of quantum entanglement. I will finally describe a possible theoretical route towards developing a classification of dynamical universality classes in many-body systems.