We demonstrate that the normalised localization length $\beta$ of the eigenfunctions of diluted (sparse) banded random matrices follows the scaling law $\beta=x^*/(1+x^*)$. The scaling parameter of the model is defined as $x^*\propto(b_{ eff}^2/N)^\delta$, where $b_{ eff}$ is the average number of non-zero elements per matrix row, $N$ is the matrix size, and $\delta\sim 1$. Additionally, we show that $x^*$ also scales the spectral properties of the model (up to certain sparsity) characterized by the spacing distribution of eigenvalues.
Categories: cond-mat.dis-nn