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 banded random matrix model 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. Therefore, we provide a full picture of the power-law banded random matrix model corresponding to the three classical Wigner–Dyson ensembles.

我们为三个经典的Wigner-Dyson合奏中的第三个（即辛合奏）引入了幂律带状随机矩阵模型。提出了对其特征向量和特征值在临界状态下的统计特性的详细分析。该合奏与具有强烈自旋轨道相互作用的时间反转对称系统有关。为了完整起见，我们还回顾了先前存在于文献中的，在存在和不存在时间反转不变性的情况下，幂律带状随机矩阵模型的特征向量和特征值的统计特性。我们的研究结果表明，对于临界状态下的本征态和本征能量统计，启发式关系具有很好的一致性，这是先前研究中提出的。所以，