LOCAL ELECTRONIC-PROPERTIES OF ONE-DIMENSIONAL QUASI-PERIODIC SYSTEMS

An exact real-space renormalization-group approach is developed to calculate the local Green's function and the local density of states at any site in an infinite Fibonacci chain, in which three basic renormalization transformations T-alpha, T-beta, and T-gamma are introduced. Transformations T-beta and T-gamma divide the Fibonacci chains of different generations into two distinct subclasses with key sites S-beta and S-gamma, respectively. The local Green's function and the local density of states at the key site S-beta or S-gamma can be obtained by successive iterations of the transformation T-beta or T-gamma. Any other site can be transferred to the key site of a renormalized Fibonacci chain by suitable combinations of the transformations T-alpha, T-beta, and T-gamma. In this approach, the relevant scale concerning the key site is tau-2, where tau is the golden mean.