PreprintCC BY 4.0arXiv
Fibonacci number systems and the localization criterion in the many-body Aubry-André model
Abstract
We introduce an extension of the Fibonacci number system, we call the fractional Fibonacci number system, which interpolates between the Fibonacci number system (used for natural numbers) and the irrational base-ϕ number system, which can be used to represent real numbers. The number system finds its use in interpreting the localization phase diagram of the many-body non-interacting Aubry-André model. For finite system sizes a localization criterion can be obtained if the particle density is written in the fractional Fibonacci number system. In the thermodynamic limit, the criterion remains, but in this case the particle density is expressed in base-ϕ. The nature of the thermodynamic limit is also discussed.
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BibTeX
@misc{hetenyi2026fibonacci,
title = {{Fibonacci number systems and the localization criterion in the many-body Aubry-André model}},
author = {Balázs Hetényi},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.03458},
eprint = {2608.03458},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.03458},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fibonacci number systems and the localization criterion in the many-body Aubry-André model
AU - Balázs Hetényi
PY - 2026
DA - 2026/08/04
PB - arXiv
DO - 10.48550/arxiv.2608.03458
UR - https://arxiv.org/abs/2608.03458
AB - We introduce an extension of the Fibonacci number system, we call the fractional Fibonacci number system, which interpolates between the Fibonacci number system (used for natural numbers) and the irrational base-ϕ number system, which can be used to represent real numbers. The number system finds its use in interpreting the localization phase diagram of the many-body non-interacting Aubry-André model. For finite system sizes a localization criterion can be obtained if the particle density is written in the fractional Fibonacci number system. In the thermodynamic limit, the criterion remains, but in this case the particle density is expressed in base-ϕ. The nature of the thermodynamic limit is also discussed.
ER -