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

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-reve...

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Bibliographic Details
Published in:arXiv.org 2021-04
Main Authors: Carrera-Núñez, M, Martínez-Argüello, A M, Méndez-Bermúdez, J A
Format: Article
Language:English
Subjects:
Eigenvalues
Eigenvectors
Fractal geometry
Mathematical analysis
Matrix
Matrix methods
Power law
Properties (attributes)
Spin-orbit interactions
Symmetry
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1908.07950