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

Author

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  • Carrera-Núñez, M.
  • Martínez-Argüello, A.M.
  • Méndez-Bermúdez, J.A.

Abstract

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.

Suggested Citation

  • Carrera-Núñez, M. & Martínez-Argüello, A.M. & Méndez-Bermúdez, J.A., 2021. "Multifractal dimensions and statistical properties of critical ensembles characterized by the three classical Wigner–Dyson symmetry classes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    • Handle: RePEc:eee:phsmap:v:573:y:2021:i:c:s0378437121002375
    DOI: 10.1016/j.physa.2021.125965
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