Probing Slow Scrambling in MBL and the Random Singlet Phase

We characterize the spreading of operators and entanglement in two paradigmatic non-thermalizing phases - the many body localized phase and the random singlet phase - using out-of-time-ordered correlators, the entanglement contour, and operator entanglement. We contrast these phases with strongly thermalizing holographic conformal field theories and fully localized Anderson insulators. We obtain a phenomenological description of the operator and state dynamics of these phases and provide credence to the utility of the entanglement contour and operator entanglement measures as useful probes of slowly scrambling and non-thermalizing dynamics.