Dynamic structure factor of a Fibonacci lattice: A renormalization-group approach.

Abstract

We present a real-space renormalization-group method for evaluating the exact dynamic structure factor S(q,\ensuremath{\omega}) of a quasiperiodic Fibonacci chain. Contrary to earlier work that takes account only of the global aspects of the symmetry of the chain, our method additionally takes care of the local environmental aspects of the symmetry by separating the original lattice into a finite number of self-similar interpenetrating sublattices, followed by elimination of the coupling between them. Our method also yields correctly the positions of the Bragg peaks of the Fibonacci chain. Moreover, the present method allows the sites of the chain to be grouped into classes following a ``genealogical'' classification, the members of a given class being equivalent up to a certain length scale. Based on this classification, the proof of the existence of a key site, which has only been conjectured in our earlier work using numerical search, has been given.