Periodic features in the Dynamic Structure Factor of the Quasiperiodic Period-doubling Lattice

TL;DR

This paper introduces an exact RSRG method to analyze the dynamic structure factor of a quasiperiodic PD lattice, revealing hierarchical Brillouin zones and delocalized phonon modes.

Contribution

It provides a novel exact real-space renormalization group approach to evaluate the dynamic structure factor in quasiperiodic lattices, uncovering hierarchical Brillouin zones and phonon mode properties.

Findings

Dynamic structure factor exhibits periodicity in wave vector q.

Presence of delocalized phonon modes in the quasiperiodic chain.

Hierarchical structure of Brillouin zones and nested dispersion curves.

Abstract

We present an exact real-space renormalization group (RSRG) method for evaluating the dynamic structure factor of an infinite one-dimensional quasiperiodic period-doubling (PD) lattice. We observe that for every normal mode frequency of the chain, the dynamic structure factor $S(q,\omega)$ always exhibits periodicity with respect to the wave vector $q$ and the presence of such periodicity even in absence of translational invariance in the system is quite surprising. Our analysis shows that this periodicity in $S(q,\omega)$ actually indicates the presence of delocalized phonon modes in the PD chain. The Brillouin Zones of the lattice are found to have a hierarchical structure and the dispersion relation gives both the acoustic as well as optical branches. The phonon dispersion curves have a nested structure and we have shown that it is actually the superposition of the dispersion curves of an infinite set of periodic lattices.