  We treat disordered Heisenberg model in 1D as the "standard model" of
many-body localization (MBL). Two independent order parameters stemming purely
from the half-chain von Neumann entanglement entropy $S_{\textrm{vN}}$ are
introduced to probe its eigenstate transition. From symmetry-endowed entropy
decomposition, they are probability distribution deviation $|d(p_n)|$ and von
Neumann entropy $S_{\textrm{vN}}^{n}(D_n\!=\!\mbox{max})$ of the
maximum-dimensional symmetry subdivision. Finite-size analyses reveal that
$\{p_n\}$ drives the localization transition, preceded by a thermalization
breakdown transition governed by $\{S_{\textrm{vN}}^{n}\}$. For noninteracting
case, these transitions coincide, but in interacting situation they separate.
Such separability creates an intermediate phase region and may help
discriminate between the Anderson and MBL transitions. An obstacle whose
solution eludes community to date is the violation of Harris criterion in
nearly all numeric investigations of MBL so far. Upon elucidating the mutually
independent components in $S_{\textrm{vN}}$, it is clear that previous studies
of eigenspectra, $S_{\textrm{vN}}$, and the like lack resolution to pinpoint
(thus completely overlook) the crucial internal structures of the transition.
We show, for the first time, that after this necessary decoupling, the
universal critical exponents for both transitions of $|d(p_n)|$ and
$S_{\textrm{vN}}^{n}(D_n\!=\!\mbox{max})$ fulfill the Harris criterion:
$\nu\approx2.0\ (\nu\approx1.5)$ for quench (quasirandom) disorder. Our work
puts forth "symmetry combined with entanglement" as the missing organization
principle for the generic eigenstate matter and transition.
