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arXiv · 1507.03434

Analysis of localization-delocalization transitions in corner-sharing tetrahedral lattices

Martin Puschmann·Philipp Cain·Michael Schreiber
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Abstract

We study the critical behavior of the Anderson localization-delocalization transition in corner-sharing tetrahedral lattices. We compare our results obtained by three different numerical methods namely the multifractal analysis, the Green resolvent method, and the energy-level statistics which yield the singularity strength, the decay length of the wave functions, and the (integrated) energy-level distribution, respectively. From these measures a finite-size scaling approach allows us to determine the critical parameters simultaneously. With particular emphasis we calculate the propagation of the statistical errors by a Monte-Carlo method. We find a high agreement between the results of all methods and we can estimate the highest critical disorder $W_\mathrm{c}=14.474(8)$ at energy $E_\mathrm{c}=-4.0$ and the critical exponent $\nu=1.565(11)$. Our results agree with a previous study by Fazileh et al. but improve accuracy significantly.

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Martin Puschmann, Philipp Cain, Michael Schreiber. 2015-07-13. Analysis of localization-delocalization transitions in corner-sharing tetrahedral lattices. https://doi.org/10.1140/epjb/e2015-60562-x

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