Exact real-space renormalization-group approach for the local electronic Green’s functions on an infinite Fibonacci chain

Abstract

We present a new real-space renormalization-group (RSRG) scheme for finding exactly the local Green's functions (LGF) for electrons in a quasiperiodic Fibonacci chain. It has been possible to construct the RSRG transformation, which, apart from renormalizing the Fibonacci chain globally, also preserves the local environment around any chosen site at which the LGF is being found. The relevant scale factor in this work is ${\ensuremath{\tau}}^{3}$, where \ensuremath{\tau} is the golden ratio. The present work gives an alternative confirmation of the Cantor-set-like behavior of the energy spectrum of the Fibonacci chain.