  Information scrambling refers to the unitary dynamics that quickly spreads
and encodes localized quantum information over an entire many-body system and
makes the information accessible from any small subsystem. While information
scrambling is the key to understanding complex quantum many-body dynamics and
is well-understood in random unitary models, it has been hardly explored in
Hamiltonian systems. In this Letter, we investigate the information recovery in
various time-independent Hamiltonian systems, including chaotic spin chains and
Sachdev-Ye-Kitaev (SYK) models. We show that information recovery is possible
in certain, but not all, chaotic models, which highlights the difference
between information recovery and quantum chaos based on the energy spectrum or
the out-of-time-ordered correlators. We also show that information recovery
probes transitions caused by the change of information-theoretic features of
the dynamics.
