Strong-disorder renormalization group approach to the Anderson model using Raleigh-Schr\"odinger perturbation theory

Abstract

Previous work proposed a strong-disorder renormalization approach for the Anderson model, using it to calculate the density of states and the inverse participation ratio [Johri \& Bhatt, Phys.\ Rev.\ B {\bf 90} 060205(R) (2014)]. This is interesting because of the potential for expansion to higher dimensions and to interacting systems. The original proposal used a non-standard perturbation theory approach which avoided degeneracies. We implemented the same structure but with standard Rayleigh-Schr\"odinger perturbation theory. Here degeneracies do arise, and we consider two approaches, one in which renormalization is suppressed if degeneracy is present and a second in which the most common form of degeneracy is handled using standard degenerate perturbation theory. The version in which degeneracies are not handled performs similarly to the original proposal, and the addition of degeneracies provides some improvement.