The real-space renormalization group and generating function for Penrose lattices

Abstract

We present a real-space renormalization group (RG) approach to study the electronic properties of the two-dimensional Penrose tilings. This approach is based on a recursive evaluation of the generating function which gives the density of states (DOS) of the system. The RG equations are derived in terms of the inflation rules of the Penrose tilings and the calculated DOS matches the results derived by purely numerical methods.