  Many aspects of many-body localization (MBL), including dynamic
classification of MBL phases, remain elusive. Here, by performing real-space
renormalization group (RSRG) analysis we propose that there are two distinct
types of MBL phases: "strong MBL" induced by quasiperiodic (QP) potential and
"weak MBL" induced by random potential. Strong and weak MBL phases can be
distinguished by their different probability distributions of thermal inclusion
and entanglement entropy: exponential decay in strong MBL phases but power-law
decay in weak MBL. We further discuss underlying mechanisms as well as
experimental implications of having two distinct types of MBL phases. Strong
MBL induced by QP potential may provide a more robust and promising platform
for quantum information storage and processing.
