Eur. Phys. J. B (2014) 87: 286
https://doi.org/10.1140/epjb/e2014-50397-4

Regular Article

Localization phase diagram of two-dimensional quantum percolation

Department of Physics, Purdue University, West Lafayette, IN 47907, USA

^a e-mail: dillonb@purdue.edu
^b e-mail: hisao@purdue.edu

Received: 12 June 2014
Received in final form: 22 October 2014
Published online: 1 December 2014

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.