Scrambling of quantum information in quantum many-body systems

Dynamics of quantum information in isolated systems is a topic of active researches, in terms of not only the foundation of statistical mechanics but also information paradox of black holes. Especially, it is significant to investigate scrambling (or delocalizing) processes of quantum information encoded in quantum many-body systems, which can be quantified by the negativity of tripartite mutual information (TMI) or the decay rate of out-of-time-ordered correlator.
In this study, we systematically investigate dynamics of TMI in quantum many-body systems by using numerical exact diagonalization. By studying quantum spin chains, we clarify that scrambling is an independent property of integrability of Hamiltonians; TMI becomescan be negative for most of the initial states, or positive for both integrable and non-integrable system, making a sharp contrast to conventional quantum chaos. In addition,Furthermore, we calculate TMI in the Sachdev-Ye-Kitaev model with four-body and disordered interaction of complex fermions, and. Wwe foundfind that disorder does not lead to slow dynamics but instead makes scrambling smoother than a clean case.
Reference: E. Iyoda and T. Sagawa, arXiv:1704.04850.