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Quantum percolation in power-law diluted chains

Rodrigo P. A. Lima·Marcelo L. Lyra
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Abstract

We investigate the quantum percolation problem in a diluted chain with long-range hopping amplitudes. Each bond is activated with probability $p(r) = p_1/r^α$, where $r$ is the distance between two sites and $α$ 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 $α< 1.5$. In the regime of $1.5 < α<2.0$ 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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Rodrigo P. A. Lima, Marcelo L. Lyra. 2001-03-26. Quantum percolation in power-law diluted chains. https://doi.org/10.1016/s0378-4371(01)00196-0

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