Abstract:
I will review some recent works on the application of RG ideas to localization problems in cases in which they have not been applied before. In particular, I will show what happens to the flow in the Anderson model when the number of dimensions tend to infinity, and how to reconstruct the flow from numerical data using the finite-size scaling theory; I will also show how different models of MBL can present different RG flows which reflect different mechanisms for the localization-ETH transition.
 
Work based on:
[1] Renormalization group analysis of the Anderson model on random regular graphs, C Vanoni, BL Altshuler, VE Kravtsov, A Scardicchio
Proceedings of the National Academy of Sciences 121 (29), e2401955121.
[2] Renormalization group for Anderson localization on high-dimensional lattices, BL Altshuler, VE Kravtsov, A Scardicchio, P Sierant, C Vanoni, arXiv preprint arXiv:2403.01974
[3] Renormalization-Group Analysis of the Many-Body Localization Transition in the Random-Field XXZ Chain, J Niedda, GB Testasecca, G Magnifico, F Balducci, C Vanoni, A Scardicchio, arXiv preprint arXiv:2410.12430
[4] Universality in Anderson localization on random graphs with varying connectivity, P Sierant, M Lewenstein, A Scardicchio, SciPost Physics 15 (2), 045