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

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.

References in corpus (6)

• Anderson Transitions
• Critical exponent for the Anderson transition in the three dimensional orthogonal universality class
• Multifractal analysis of the metal-insulator transition in the 3D Anderson model I: Symmetry relation under typical averaging
• Multifractal analysis of the metal-insulator transition in the 3D Anderson model II: Symmetry relation under ensemble averaging
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Cited by in corpus (1)

• Green's functions on a renormalized lattice: An improved method for the integer quantum Hall transition