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Quantum percolation in power-law diluted chains

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  • Lima, R.P.A.
  • Lyra, M.L.

Abstract

We investigate the quantum percolation problem in a diluted chain with long-range hopping amplitudes. Each bond is activated with probability p(r)=p1/rα, 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 p1(q), true extended states appear for α<1.5. In the regime of 1.5<α<2.0 there is no truly extended states even in the presence of a spanning cluster. Instead, a phase of critical wave-functions sets up.

Suggested Citation

  • Lima, R.P.A. & Lyra, M.L., 2001. "Quantum percolation in power-law diluted chains," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 297(1), pages 157-163.
    • Handle: RePEc:eee:phsmap:v:297:y:2001:i:1:p:157-163
    DOI: 10.1016/S0378-4371(01)00196-0
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