Eur. Phys. J. B (2015) 88: 275
https://doi.org/10.1140/epjb/e2015-60562-x

Regular Article

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

Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany

^a e-mail: martin.puschmann@physik.tu-chemnitz.de

Received: 13 July 2015
Received in final form: 4 September 2015
Published online: 26 October 2015

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_c = 14.474 (8) at energy E_c = − 4.0 and the critical exponent ν = 1.565 (11). Our results agree with a previous study by Fazileh et al. [F. Fazileh, X. Chen, R.J. Gooding, K. Tabunshchyk, Phys. Rev. B 73, 035124 (2006)] but improve accuracy significantly.