  We introduce a power-law banded random matrix model for the third of the
three classical Wigner-Dyson ensembles, i.e., the symplectic ensemble. A
detailed analysis of the statistical properties of its eigenvectors and
eigenvalues, at criticality, is presented. This ensemble is relevant for
time-reversal symmetric systems with strong spin-orbit interaction. For the
sake of completeness, we also review the statistical properties of eigenvectors
and eigenvalues of the power-law random banded matrix model for the
corresponding systems in the presence and absence of time reversal invariance,
previously considered in the literature. Our results show a good agreement with
heuristic relations for the eigenstate and eigenenergy statistics at
criticality, proposed in previous studies. With this, we provide a full picture
of the power-law random banded matrix model corresponding to the three
classical Wigner-Dyson ensembles.
