Initial-state dependence of out-of-time-ordered correlator in many-body localization

Abstract

We investigate the characteristics of out-of-time-ordered correlator (OTOC) time-evolving from a prepared initial state in a disordered spin-1/2 XXZ Heisenberg chain. While an evaluation of OTOC has been previously suggested as an indicator of many-body localization, we find that a specific preparation of the initial state may largely affect the dynamics of the OTOC distribution across random disorder realizations. It turns out that the distribution of OTOC exhibits two distinctive patterns in its time evolution where the one just spreads out without an well-defined average while the other becomes very spiky with a meaningful average over different realizations of disorder. We discuss its possible implications on the typicality of initial- state preparation for experiments with ultracold quantum gases.