Multifractal dimensions and statistical properties of critical ensembles characterized by the three classical Wigner–Dyson symmetry classes

• Published in: Physica A Vol. 573; p. 125965
• Main Authors: Carrera-Núñez, M., Martínez-Argüello, A.M., Méndez-Bermúdez, J.A.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.07.2021
• Subjects: Disordered systems; Finite-size scaling; Metal–insulator transitions; Metal–insulator transitions; Disordered systems; Finite-size scaling
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2021.125965

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.