Anderson localization and ergodicity on random regular graphs

Article

关键词: METAL-INSULATOR-TRANSITION;    MANY-BODY LOCALIZATION;    QUASI-PARTICLE LIFETIME;    LEVEL STATISTICS;    QUANTUM-DOT;    DISORDERED-SYSTEMS;    BETHE LATTICE;    GRADED SYMMETRY;    FERMI SYSTEMS;    FOCK-SPACE;   

DOI  :  10.1103/PhysRevB.94.220203

来源: SCIE

【 摘 要 】

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 N sites that is locally a tree with constant connectivity. In a certain sense, the RRG ensemble can be seen as an infinite-dimensional (d -> infinity) cousin of the Anderson model in d 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 (N << N-c) to a large (N >> N-c) system, where Nc 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 N >> N-c) are ergodic in the sense that their inverse participation ratio scales as 1/N.

【 授权许可】

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