Hidden Dimer in the Frenkel-Kontorova model

TL;DR

This paper reveals a hidden dimer structure in the Frenkel-Kontorova model that leads to unique excitations called stepon modes, potentially influencing localization phenomena in disordered systems.

Contribution

It introduces the concept of a hidden dimer in the Frenkel-Kontorova model and links it to Bloch-wave excitations and localization boundary implications.

Findings

Identification of a hidden dimer structure in the model

Discovery of stepon modes as multi-step phonon excitations

Potential role of these modes in Anderson localization boundaries

Abstract

The incommensurability of the supercritical Frenkel-Kontorova model is decomposed into a family of dimer type "defects" by appropriate decimations. Interestingly, this hidden dimer results in Bloch-wave type excitations of the renormalized chain which appear in the disguised form of multi-step phonon modes for the original system. We call these intriguing excitations stepon modes and conjecture that they play a key role in determining the localization boundary in systems exhibiting Anderson localization.