Transition between localized and extended states in the hierarchical Anderson model

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	Transition between localized and extended states in the hierarchical Anderson model
	Metz, FL ; Leuzzi, L ; Parisi, G ; Sacksteder, V
刊名	PHYSICAL REVIEW B
	2013
卷号	88 期号:4
ISSN号	1098-0121
通讯作者	Metz, FL (reprint author), Univ Roma La Sapienza, Dipartimento Fis, Piazzale A Moro 2, I-00185 Rome, Italy.
中文摘要	We present strong numerical evidence for the existence of a localization-delocalization transition in the eigenstates of the 1D Anderson model with long-range hierarchical hopping. Hierarchical models are important because of the well-known mapping between their phases and those of models with short-range hopping in higher dimensions, and also because the renormalization group can be applied exactly without the approximations that generally are required in other models. In the hierarchical Anderson model, we find a finite critical disorder strength W-c where the average inverse participation ratio goes to zero; at small disorder, W < W-c, the model lies in a delocalized phase. This result is based on numerical calculation of the inverse participation ratio in the infinite volume limit using an exact renormalization group approach facilitated by the model's hierarchical structure. Our results are consistent with the presence of an Anderson transition in short-range models with D > 2 dimensions, which was predicted using renormalization group arguments. Our finding should stimulate interest in the hierarchical Anderson model as a simplified and tractable model of the Anderson localization transition, which occurs in finite-dimensional systems with short-range hopping.
资助信息	European Research Council (ERC) [247328]; European Union [290038]; Italian MIUR [RBFR08M3P4, 2010HXAW77-008]
语种	英语
公开日期	2014-01-17
内容类型	期刊论文
源URL	[http://ir.iphy.ac.cn/handle/311004/57620]
专题	物理研究所_物理所公开发表论文_物理所公开发表论文_期刊论文
推荐引用方式 GB/T 7714	Metz, FL,Leuzzi, L,Parisi, G,et al. Transition between localized and extended states in the hierarchical Anderson model[J]. PHYSICAL REVIEW B,2013,88(4).
APA	Metz, FL,Leuzzi, L,Parisi, G,&Sacksteder, V.(2013).Transition between localized and extended states in the hierarchical Anderson model.PHYSICAL REVIEW B,88(4).
MLA	Metz, FL,et al."Transition between localized and extended states in the hierarchical Anderson model".PHYSICAL REVIEW B 88.4(2013).