  We employ the power-law random band matrix (PRBM) ensemble with single tuning
parameter $\mu $ as the effective model for many-body localization (MBL)
transition in random spin systems. We show the PRBM accurately reproduce the
eigenvalue statistics on the entire phase diagram through the fittings of
high-order spacing ratio distributions $P(r^{(n)})$ as well as number variance
$\Sigma ^{2}(l)$, in systems both with and without time-reversal symmetry. For
the properties of eigenvectors, it's shown the entanglement entropy of PRBM
displays an evolution from volume-law to area-law behavior which signatures an
ergodic-MBL transition, and the critical exponent is found to be $\nu =0.83\pm
0.15$, close to the value obtained in 1D physical model by exact
diagonalization while the computational cost here is much less.
