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Updated: Jun 21, 2025
09:19
Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light
Published on: July 29, 2013
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Renormalization group analysis of the Anderson model on random regular graphs
Carlo Vanoni1,2, Boris L Altshuler3, Vladimir E Kravtsov4
1International School for Advanced Studies, Trieste 34136, Italy.
Summary
We analyzed Anderson localization on random regular graphs using renormalization group methods. Our findings explain unusual scaling behaviors in disorder systems and support the one-parameter scaling hypothesis for large system sizes.
Area of Science:
- Condensed Matter Physics
- Statistical Mechanics
- Disordered Systems
Background:
- Anderson localization describes the suppression of wave function propagation in disordered systems.
- Random Regular Graphs (RRGs) offer a simplified model for studying localization in high dimensions.
- Previous renormalization group (RG) studies have limitations in capturing complex scaling behaviors.
Purpose of the Study:
- To extend the renormalization group (RG) analysis to Anderson localization on random regular graphs (RRGs).
- To investigate the validity of the one-parameter scaling hypothesis in this context.
- To explain the nonmonotonic behavior of physical quantities near the localization transition.
Main Methods:
- A generalized renormalization group (RG) analysis was applied to the Anderson model on RRGs.
- The RG equations were analyzed to understand the flow of parameters with changing connectivity.
- The beta function for the running fractal dimension was derived and analyzed.
Main Results:
- The one-parameter scaling hypothesis is recovered for large system sizes for both eigenstates and spectral observables.
- Two terms with differing signs and dependencies in the beta function explain nonmonotonic behaviors.
- The RG analysis provides a coherent explanation for observed numerical data in Anderson localization on RRGs.
Conclusions:
- The developed RG theory successfully explains the complex scaling observed in Anderson localization on RRGs.
- The study reconciles theoretical predictions with numerical findings for disordered systems.
- This framework offers insights into many-body localization phenomena.
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