Quantum information scrambling and quantum chaos in little string theory

Abstract

In the current manuscript we perform a systematic investigation about the effects of nonlocal interaction to the spread of quantum information in many body system. In particular, we have studied how nonlocality influence the existing bound on the growth rate of the commutator involving two local operators, the butterfly velocity. For this purpose, we consider the nonlocal theory on the worldvolume of $N\gg 1$, NS$5$ branes arising in the limit of vanishing string coupling, the `little string theory'. A direct evidence of nonlocality can be realized from the `volume law' behavior for the most dominant part of holographic entanglement entropy. We obtain the butterfly velocity by studying the dynamics of the near horizon geometry backreacted by a high energy quanta in the form of a shockwave resulting from an early perturbation on the corresponding thermofield double state. We observe that the butterfly velocity increases with the nonlocal scale of little string theory, the inverse Hagedorn temperature $β_{h}$, indicating a faster rate of information spread due to the nonlocal interaction. The same conclusion follows as the disruption of two sided mutual information is observed to occur at a faster rate for higher values of $β_{h}$. Finally, we realize a direct connection between the parameters of quantum chaos and the quasinormal modes for collective excitations through the phenomenon of `pole skipping'.