Logarithmic spreading of out-of-time-ordered correlators without many-body localization

Understand

Out-of-time-ordered correlators (OTOCs) describe information scrambling under unitary time evolution, and provide a useful probe of the emergence of quantum chaos.

• Here we calculate OTOCs for a model of disorder-free localization whose exact solubility allows us to study long-time behaviour in large systems.
• Remarkably, we observe logarithmic spreading of correlations, qualitatively different to both thermalizing and Anderson localized systems.
• Rather, such behaviour is normally taken as a signature of many-body localization, so that our findings for an essentially non-interacting model are surprising.