Localization phase diagram of two-dimensional quantum percolation

Brianna S. Dillon () and Hisao Nakanishi ()

The European Physical Journal B: Condensed Matter and Complex Systems, 2014, vol. 87, issue 12, 1-9

Abstract: We examine quantum percolation on a square lattice with random dilution up to q=38% and energy 0.001 ≤ E ≤ 1.6 (measured in units of the hopping matrix element), using numerical calculations of the transmission coefficient at a much larger scale than previously. Our results confirm the previous finding that the two dimensional quantum percolation model exhibits localization-delocalization transitions, where the localized region splits into an exponentially localized region and a power-law localization region. We determine a fuller phase diagram confirming all three regions for energies as low as E=0.1, and the delocalized and exponentially localized regions for energies down to E=0.001. We also examine the scaling behavior of the residual transmission coefficient in the delocalized region, the power law exponent in the power-law localized region, and the localization length in the exponentially localized region. Our results suggest that the residual transmission at the delocalized to power-law localized phase boundary may be discontinuous, and that the localization length is likely not to diverge with a power-law at the exponentially localized to power-law localized phase boundary. However, further work is needed to definitively assess the characters of the two phase transitions as well as the nature of the intermediate power-law regime. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014

Keywords: Statistical and Nonlinear Physics (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1140/epjb/e2014-50397-4

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