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For the characterization of the dynamics in quantum many-body systems thequestion how information spreads and becomes distributed over the constituentdegrees of freedom is of fundamental interest. The delocalization ofinformation under many-body dynamics has been dubbed scrambling andout-of-time-order correlators were proposed to probe this behavior. In thiswork we investigate the time-evolution of tripartite information as a naturaloperator-independent measure of scrambling, which quantifies to which extentthe initially localized information can only be recovered by globalmeasurements. Studying the dynamics of quantum lattice models with tunableintegrability breaking we demonstrate that in contrast to quadratic modelsgeneric interacting systems scramble information irrespective of the chosenpartitioning of the Hilbert space, which justifies the characterization asscrambler. Without interactions the dynamics of tripartite information inmomentum space reveals unambiguously the absence of scrambling.

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