Diluted banded random matrices: scaling behavior of eigenfunction and spectral properties

• Published in: Journal of physics. A, Mathematical and theoretical Vol. 50; no. 49; pp. 495205 - 495214
• Main Authors: Méndez-Bermúdez, J A, de Arruda, Guilherme Ferraz, Rodrigues, Francisco A, Moreno, Yamir
• Format: Journal Article
• Language: English
• Published: IOP Publishing 08.12.2017
• Subjects: localization length of eigenfunctions; random matrix theory; scaling laws; wigner-banded random matrix model
• ISSN: 1751-8113; 1751-8121
• DOI: 10.1088/1751-8121/aa9509

We demonstrate that the normalized localization length β of the eigenfunctions of diluted (sparse) banded random matrices follows the scaling law β=x∗/(1+x∗). The scaling parameter of the model is defined as x∗∝(beff2/N)δ, where beff is the average number of non-zero elements per matrix row, N is the matrix size, and δ∼1. Additionally, we show that x∗ also scales the spectral properties of the model (up to certain sparsity) characterized by the spacing distribution of eigenvalues.