Renormalization Group Analysis of the Anderson Model on Random Regular Graphs

Carlo Vanoni, Boris L. Altshuler, Vladimir E. Kravtsov, Antonello Scardicchio
Condensed Matter, Disordered Systems and Neural Networks, Disordered Systems and Neural Networks (cond-mat.dis-nn), Statistical Mechanics (cond-mat.stat-mech), Quantum Physics (quant-ph)
2023-06-25 16:00:00
We present a renormalization group analysis of the problem of the Anderson localization on a Random Regular Graph which generalizes the renormalization group of Abrahams, Anderson, Licciardello, and Ramakrishnan to infinite-dimensional graphs. The renormalization group equations necessarily involve two parameters (one being the changing connectivity of sub-trees), but we show that the one-parameter scaling hypothesis is recovered for sufficiently large system sizes for both eigenstates and spectrum observables. We also explain the non-monotonic behavior of dynamical and spectral quantities as a function of the system size for values of disorder close to the transition, by identifying two terms in the beta function of the running fractal dimension of different signs and functional dependence. Our theory provides the first coherent explanation for the unusual scaling behaviors observed in numerical data of the Anderson model and of Many-Body Localization.
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