Quantum percolation of one-electron states in power-law diluted chains

Abstract

We investigate the nature of one-electron eigenstates in power-law diluted chains for which the probability of occurrence of a bond between sites separated by a distance r decays as p(r) = 1/r 1+σ . Using an exact diagonalization scheme on finite chains, we compute the spreading of an initially localized wave-packet, the time dependent participation number as well as the return probability. Our results show the existence of a phase of extended states. By considering the scale invariance of the fluctuations of the participation number at the Anderson transition, we obtained that extended states emerges for σ < 0.68. This limiting value is larger than the one reported in the literature for the emergence of extended states in one-dimensional Anderson models with power-law decaying couplings.