Level-spacing distribution of a fractal matrix
arXiv:cond-mat/0111080 · doi:10.1016/S0375-9601(01)00593-X
Abstract
We diagonalize numerically a Fibonacci matrix with fractal Hilbert space structure of dimension We show that the density of states is logarithmically normal while the corresponding level-statistics can be described as critical since the nearest-neighbor distribution function approaches the intermediate semi-Poisson curve. We find that the eigenvector amplitudes of this matrix are also critical lying between extended and localized.
6 pages, Latex file, 4 postscript files, published in Phys. Lett. A289 pp 183-7 (2001)