Criticality without self-similarity: a 2D system with random long-range hopping

Details Criticality without self-similarity: a 2D system with random long-range hopping Criticality without self-similarity: a 2D system with random long-range hopping

2011-01-13

arxiv.org/abs/1101.2641v2

J. Phys.: Condens. Matter 23 (2011) 415601

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 2 figures

Scientific paper

10.1088/0953-8984/23/41/415601

We consider a simple model of quantum disorder in two dimensions, characterized by a long-range site-to-site hopping. The system undergoes a metal-insulator transition -- its eigenfunctions change from being extended to being localized. We demonstrate that at the point of the transition the eigenfunctions do not become fractal. Their density moments do not scale as a power of the system size. Instead, in one of the considered limits our result suggests a power of the logarithm of the system size. In this regard, the transition differs from a similar one in the one-dimensional version of the same system, as well as from the conventional Anderson transition in more than two dimensions.

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