FWF-ECOFFEQ - Entanglement and correlations far from equillibrium

In the last decade, concepts from information theory proved to be very important in understanding the physics of strongly correlated quantum many-body systems. Measures of information shared between different parts of an extended system provide an extremely useful and simple characterization of the underlying equilibrium phases of matter. The approach has been particularly successful in quantifying the quantum correlations in ground states of quantum many-body systems where several universal features emerge. At finite temperatures, the measure of mutual information has also been widely studied in equilibrium and was always found to satisfy an area law. The present research proposal aims to extend the toolbox of information theory to the study of nonequilibrium many-body systems. Through this viewpoint, we hope to gain novel insight into the mechanisms of far from equilibrium phenomena. In particular, we are interested in the study of nonequilibrium steady states of driven systems, where the emergence of strong correlations is often observed. The main question to be addressed is whether some of these steady states can violate the area law of mutual information. Furthermore, another goal is to check whether the behaviour of this measure inherits some of the universality features observed in equilibrium. Ideally, this could lead to a new characterization of nonequilibrium steady states and to the identification of their universality classes. The second part of the project is focused on the dynamical aspects of mutual information in various nonequilibrium processes, involving unitary time evolution from an initial state with inhomogeneities of e.g. the particle or energy density. Instead of looking at the steady state, which forms in the bulk of the system after long enough times, we will focus on the evolution of the front region. Particularly interesting is the case of integrable models where ballistic dynamics can lead to the formation of staircase-like front structures. The main goal is to identify the characteristic features of the mutual information in the front regime which might lead to a better understanding of the intriguing behaviour of quantum fronts.