PreprintCC BY 4.0arXiv
Quantum Metric Scaling and Its Exceptions in Classical Flat Bands
Abstract
The quantum metric length has been proposed as the localization length scale in one-dimensional flat bands. Here, we study this quantum metric scaling and the exceptions to it in a classical flat band formed by a locally resonant mass--spring system. We find that the localization length follows the quantum metric length near the flat band but departs from this proportionality at the exact flat-band frequency. Selective mass disorder also produces divergent localization lengths or arbitrarily short tails near the flat-band frequency without changing the clean metric. These exceptions show that disorder can select localization scales beyond those predicted by the quantum metric alone.
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BibTeX
@misc{fung2026quantum,
title = {{Quantum Metric Scaling and Its Exceptions in Classical Flat Bands}},
author = {Kin Hung Fung and K. T. Law and C. T. Chan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40066},
eprint = {2610.40066},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40066},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum Metric Scaling and Its Exceptions in Classical Flat Bands
AU - Kin Hung Fung
AU - K. T. Law
AU - C. T. Chan
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40066
UR - https://arxiv.org/abs/2610.40066
AB - The quantum metric length has been proposed as the localization length scale in one-dimensional flat bands. Here, we study this quantum metric scaling and the exceptions to it in a classical flat band formed by a locally resonant mass--spring system. We find that the localization length follows the quantum metric length near the flat band but departs from this proportionality at the exact flat-band frequency. Selective mass disorder also produces divergent localization lengths or arbitrarily short tails near the flat-band frequency without changing the clean metric. These exceptions show that disorder can select localization scales beyond those predicted by the quantum metric alone.
ER -