Large Disorder Renormalization Group Study of the Anderson Model of Localization

We describe a large disorder renormalization group (LDRG) scheme for the Anderson model of localization in one dimension which eliminates eigenstates based on the size of their wavefunctions rather than their energy[1] (as done in RG models to date). We show that our LDRG scheme flows to infinite disorder, and thus becomes asymptotically exact. We use it to obtain the disorder-averaged inverse participation ratio and density of states and compare these with results obtained by exact numerical diagonalization for the entire spectrum. A modified method is formulated for higher dimensions, which is found to be less efficient, but capable of improvement. The possibility of extending this scheme to many-body localized states will be discussed. 1. Sonika Johri and R. N. Bhatt, Phys. Rev. B \textbf{90}, 060205(R) (2014)