Inapplicability of Avila's theory in the diamond chain with quasiperiodic disorder
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.
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BibTeX
@misc{kumar2026inapplicability,
title = {{Inapplicability of Avila's theory in the diamond chain with quasiperiodic disorder}},
author = {Manish Kumar and Ivan M Khaymovich and Auditya Sharma},
howpublished = {HAL},
year = {2026},
month = oct,
eprint = {2603.12362},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05765884v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Inapplicability of Avila's theory in the diamond chain with quasiperiodic disorder
AU - Manish Kumar
AU - Ivan M Khaymovich
AU - Auditya Sharma
PY - 2026
DA - 2026/10/10
PB - HAL
UR - https://hal.science/hal-05765884v1
AB - 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.
ER -