Localization transition in random Lévy matrices: multifractality of eigenvectors in the localized phase and at criticality
Localization transition in random Lévy matrices: multifractality of eigenvectors in the localized phase and at criticality
For random L\'evy matrices of size $N \times N$, where matrix elements are drawn with some heavy-tailed distribution $P(H_{ij}) \propto N^{-1} |H_{ij} |^{-1-\mu}$ with $0<\mu<2$ (infinite variance), there exists an extensive number of finite eigenvalues $E=O(1)$, while the maximal eigenvalue grows as $E_{max} \sim N^{\frac{1}{\mu}}$. Here we study the localization …