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

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

Physica A: Statistical Mechanics and its Applications, 2021, vol. 573, issue C

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.

Keywords: Disordered systems; Metal–insulator transitions; Finite-size scaling (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:573:y:2021:i:c:s0378437121002375

DOI: 10.1016/j.physa.2021.125965

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