  Study how quantum information propagates through spacetime manifold provides
a means of identifying, distinguishing, and classifying novel phases of matter
fertilized by many-body effects in strongly interacting systems in and out of
equilibrium. Via a fuller characterization of key aspects regarding dynamic
behaviors of information, we perform such an analysis on constrained many-body
localization -- a newly proposed fully localized state under
infinite-interaction limit -- in quasirandom Rydberg blockade spin chain models
using thermal out-of-time-order commutators (OTOCs). The OTOC light cones
predict a hitherto unknown Lieb-Robinson bound for constrained many-body
localization, which is qualitatively different from that of unconstrained
many-body Anderson insulators stabilized at weak-interaction limit. Our
corroborated numeric and analytic study suggests that constrained many-body
localization is a distinct dynamical eigenstate phase whose nonergodicity is
beyond local-integral-of-motion phenomenology. Together, these findings
consolidate the hierarchy of unconventional quantum dynamics encompassing
constrained, unconstrained, and diagonal many-body-localized regimes.
