Quantum percolation in power-law diluted chains

Details Quantum percolation in power-law diluted chains Quantum percolation in power-law diluted chains

2001-03-26

arxiv.org/abs/cond-mat/0103545v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

6 pages + 5 figures

Scientific paper

10.1016/S0378-4371(01)00196-0

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.

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