A renormalization group analysis of the Anderson model ‌in infinite dimensions

C. Vanoni,1 B. Altshuler,2 V. Kravtsov,3 A. Scardicchio3

1SISSA – International School for Advanced Studies, via Bonomea 265, 34136, Trieste, Italy

2Physics Department, Columbia University, 538 West 120th Street, New York, New York 10027, USA

3ICTP, Strada Costiera 11, 34151, Trieste, Italy

In this talk, I will present a renormalization group analysis of the problem of Anderson localization on Regular Random Graphs (RRGs). I will first review and extend the finite-dimensional analysis of Abrahams, Anderson, Licciardello, and Ramakrishnan in terms of spectral observables, and discuss how to take the large-d limit. I will then motivate that the infinite-dimensional case, relevant also in the context of Many-Body Localization, recovers the Anderson model on RRGs. In this case, the renormalization group β-function necessarily involves two parameters, but the one-parameter scaling hypothesis is recovered for sufficiently large system sizes. I will also discuss how to understand this change in behavior in terms of the geometrical properties of the graphs. The talk will be based on arXiv:2306.14965 and ongoing work.