Inapplicability of Avila's theory in the diamond chain with quasiperiodic disorder

TL;DR

This study investigates how quasiperiodic disorder affects mobility edges in a diamond chain, revealing limitations of Avila's theory in predicting these edges and demonstrating the transformation of anomalous mobility edges.

Contribution

It shows that adding a constant offset to the quasiperiodic potential can alter mobility edges and highlights the failure of Avila's global theory to predict their locations.

Findings

Offset transforms anomalous mobility edges into conventional ones

Multiple mobility edges form, not predicted by Avila's theory

First example showing Avila's theory's limitations in this context

Abstract

The mobility edges (MEs) that separate localized, multifractal and ergodic states in energy are a central concept in understanding Anderson localization. In this work we study the effect of several mutually commensurate quasiperiodic frequencies on the mobility edge formation. We focus on the example of the addition of a constant offset to the quasiperiodic potential of the one-dimensional all-bands-flat diamond chain. We show that this additional offset can transform the anomalous mobility edges (AMEs), i.e. the energies, separating localized and multifractal states, into conventional mobility edges, separating localized from delocalized states. Also this appears to be the first example which shows the inability of Avila's global theory to analytically predict the ME location. We observe this both quantitatively, through the ME location mismatch, and qualitatively, via the formation of multiple MEs, not predicted by the theory.