Quantum percolation in power-law diluted chains

Abstract

We investigate the quantum percolation problem in a diluted chain with long-range hopping amplitudes. Each bond is activated with probability $p(r)=p_1/r^{\alpha }$, where $r$ is the distance between two sites and $\alpha$ characterizes the range of the interactions. The average participation ratio of all eigenstates is used as a measure of the wave-functions localization length. We found that, above a quantum percolation threshold $p_1^{(q)}$, true extended states appears for $\alpha <1.5$. In the regime of $1.5<\alpha <2.0$ there is no trully extended states even in the presence of a spanning cluster. Instead, a phase of critical wave-functions sets up.

6 pages + 5 figures

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