Strong-disorder renormalization group study of the Anderson localization transition in three and higher dimensions

We implement an efficient strong-disorder renormalization group (SDRG) procedure\footnote{H. Javan Mard, Jos\'{e} A. Hoyos, E. Miranda, V. Dobrosavljevi\'c, \textit{Strong-disorder renormalization-group study of the one-dimensional tight-binding model} , Phys. Rev. B 90, 125141(2014).} for disordered tight-binding models in dimension $D\ge 3$ , including the localization properties on Erd\H{o}s-R\'{e}nyi random graphs, which represent an appropriate infinite dimensional limit. Our dramatically improved SDRG algorithm is based on a judicious elimination of most (irrelevant) new bonds generated under RG. It yields excellent agreement with exact numerical results for universal properties at the critical point, without significant increase of the required computer time, even as the spatial dimension is increased beyond $D=3$. This opens an efficient avenue to explore the critical properties of Anderson transition in the strong-coupling limit of high spatial dimensions.