Entanglement and correlations far from equilibrium

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.

Understanding the dynamical features of far from equilibrium many-body quantum systems belongs to one of the big challenges of modern condensed matter physics research. Among the many approaches that have been pursued in recent decades, this project aimed at the study of dynamical behaviour of entanglement in various nonequilibrium situations. Entanglement is a genuine quantum mechanical feature, and it plays a key role in our understanding of many universal properties of equilibrium quantum matter. Our main goal was to extend the studies of entanglement to simple paradigmatic off-equilibrium scenarios. In particular, we have studied entanglement evolution in quantum spin chains, starting from a sharp domain wall, or from an inhomogeneous initial state created by a magnetic field gradient. Our main finding was that, despite being in a far from equilibrium regime, the entanglement entropy in the transverse Ising chain can still show an asymptotic area-law behaviour, similarly to the equilibrium case. On the other hand, for the gradient XXZ chain the entanglement evolution turns out to be much more complicated, and partly reflects the underlying quasi-particle picture that follows from a generalized hydrodynamic description. While in the above examples we dealt with pure states where the entanglement can be calculated via Renyi entropies, we have also studied a different entanglement measure, the so-called negativity, that is appropriate for mixed-state scenarios. Since the properties of negativity are still to a large extent unexplored, here we have restricted our scope to equilibrium situations, and we are aiming to generalize our studies to the dynamical regime in a follow-up project. In particular, we have shown that the entanglement negativity displays an area law between adjacent regions in two-dimensional ground states with bosonic degrees of freedom, while in case of fermions one finds signatures of a logarithmic area-law violation.