Abstract
A numerical study of Anderson transition on random regular graphs (RRGs) with diagonal disorder is performed. The problem can be described as a tight-binding model on a lattice with sites that is locally a tree with constant connectivity. In a certain sense, the RRG ensemble can be seen as an infinite-dimensional cousin of the Anderson model in dimensions. We focus on the delocalized side of the transition and stress the importance of finite-size effects. We show that the data can be interpreted in terms of the finite-size crossover from a small to a large system, where is the correlation volume diverging exponentially at the transition. A distinct feature of this crossover is a nonmonotonicity of the spectral and wave-function statistics, which is related to properties of the critical phase in the studied model and renders the finite-size analysis highly nontrivial. Our results support an analytical prediction that states in the delocalized phase (and at are ergodic in the sense that their inverse participation ratio scales as .
- Received 18 April 2016
- Revised 18 August 2016
DOI:https://doi.org/10.1103/PhysRevB.94.220203
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