On the multifractal dimensions and statistical properties of critical ensembles characterized by the three classical Wigner-Dyson symmetry classes

• Published in: arXiv.org
• Main Authors: Carrera-Núñez, M, Martínez-Argüello, A M, Méndez-Bermúdez, J A
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 10.04.2021
• Subjects: Eigenvalues; Eigenvectors; Fractal geometry; Mathematical analysis; Mathematics - Mathematical Physics; Matrix; Matrix methods; Physics - Disordered Systems and Neural Networks; Physics - Mathematical Physics; Power law; Properties (attributes); Spin-orbit interactions; Symmetry
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1908.07950

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.