Tripartite information, scrambling, and the role of Hilbert space partitioning in quantum lattice models

For the characterization of the dynamics in quantum many-body systems the question how information spreads and becomes distributed over the constituent degrees of freedom is of fundamental interest. The delocalization of information under many-body dynamics has been dubbed scrambling and out-of-time-order correlators were proposed to probe this behavior. In this work we investigate the time-evolution of tripartite information as a natural operator-independent measure of scrambling, which quantifies to which extent the initially localized information can only be recovered by global measurements. Studying the dynamics of quantum lattice models with tunable integrability breaking we demonstrate that in contrast to quadratic models generic interacting systems scramble information irrespective of the chosen partitioning of the Hilbert space, which justifies the characterization as scrambler. Without interactions the dynamics of tripartite information in momentum space reveals unambiguously the absence of scrambling.