Scrambling of quantum information in interacting integrable systems

Scrambling or delocalization of quantum information is an important indicator of how chaotic a many-body quantum dynamics is, and can be quantified by the Tri-partite Operator Mutual Information (TOMI), defined through the entanglement of the unitary evolution operator. While TOMI has been thoroughly studied in the contexts of systems exhibiting either simple or maximally chaotic dynamics, its behavior in systems with "intermediate" dynamics is yet to be understood. One example of such systems is the interacting integrable models, where the interplay of interactions and extensive number of conserved charges may lead to interesting scrambling behavior. Here we look at various interacting integrable models, including the XXZ spin chain and the one-dimensional Hubbard model. We begin by performing a numerical analysis of TOMI in these systems, focusing on the scaling behavior of its late-time saturation value. We then present an analytical interpretation using the recently developed tool invoking Bethe Ansatz, and make connections and comparisons with chaotic dynamics with a finite number of conserved charges.