Scaling up the Anderson transition in random-regular graphs

@article{Pino2020ScalingUT,
  title={Scaling up the Anderson transition in random-regular graphs},
  author={Manuel Pino},
  journal={arXiv: Disordered Systems and Neural Networks},
  year={2020}
}
  • M. Pino
  • Published 27 May 2020
  • Mathematics
  • arXiv: Disordered Systems and Neural Networks
We study the Anderson transition in lattices with the connectivity of a random-regular graph. Our results indicate that fractal dimensions are continuous across the transition, but a discontinuity occurs in their derivatives, implying the non-ergodicity of the metal near the Anderson transition. A critical exponent $\nu = 1.00 \pm0.02$ and critical disorder $W= 18.2\pm 0.1$ are found via a scaling approach. Our data support that the predictions of the relevant Gaussian Ensemble are only… 
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References

SHOWING 1-10 OF 106 REFERENCES
Scaling Theory of the Anderson Transition in Random Graphs: Ergodicity and Universality.
TLDR
The Anderson transition is studied on a generic model of random graphs with a tunable branching parameter 1<K<2, and a single transition separates a localized phase from an unusual delocalized phase that is ergodic at large scales but strongly nonergodic at smaller scales.
Anderson localization and ergodicity on random regular graphs
A numerical study of Anderson transition on random regular graphs (RRG) with diagonal disorder is performed. The problem can be described as a tight-binding model on a lattice with N sites that is…
Return probability for the Anderson model on the random regular graph
We show that comparing typical and mean values of the return probability one can differentiate between ergodic and multifractal dynamical phases in some random matrix model (power-law random banded…
Critical behavior at the localization transition on random regular graphs
We study numerically the critical behavior at the localization transition in the Anderson model on infinite Bethe lattice and on random regular graphs. The focus is on the case of coordination number…
Two critical localization lengths in the Anderson transition on random graphs
We present a full description of the nonergodic properties of wavefunctions on random graphs without boundary in the localized and critical regimes of the Anderson transition. We find that they are…
Anomalously large critical regions in power-law random matrix ensembles.
TLDR
It is found that for macroscopic samples there exists a finite critical region, in which this length is larger than the system size, and the Green's functions decrease with distance as a power law with an exponent related to the correlation dimension.
Anderson localization on the Bethe lattice: nonergodicity of extended States.
Statistical analysis of the eigenfunctions of the Anderson tight-binding model with on-site disorder on regular random graphs strongly suggests that the extended states are multifractal at any finite…
A random matrix model with localization and ergodic transitions
Motivated by the problem of many-body localization and the recent numerical results for the level and eigenfunction statistics on the random regular graphs, a generalization of the Rosenzweig–Porter…
Spread of wave packets in disordered hierarchical lattices
We consider the spreading of a wave packet in the generalized Rosenzweig-Porter random matrix ensemble in the region of the non-ergodic extended states . We show that although non-trivial fractal…
Critical parameters from a generalized multifractal analysis at the Anderson transition.
We propose a generalization of multifractal analysis that is applicable to the critical regime of the Anderson localization-delocalization transition. The approach reveals that the behavior of the…
...
...