Collective Modes of Fractional States Beyond Landau Levels
Abstract
Collective modes provide a powerful probe into the properties and stability of topologically ordered and strongly interacting phases of matter, such as fractional quantum Hall states. Yet, the description of fractional-state excitations away from the Landau-level limit remains a formidable challenge. We develop a framework for describing collective excitations in the strong-coupling regime of coupled-wire constructions and show that they emerge as solitons and breathers of effective sine-Gordon theories. This approach provides a systematic route to studying collective modes in a broad class of fractional states. Applied to a coupled-wire construction of the fractional quantum Hall effect, the framework captures key features of the magnetoroton branch. It naturally extends to fractional Chern insulators, demonstrating that magnetoroton-like collective modes persist well beyond the Landau-level limit. We find that the magnetoroton gap increases as the Fubini-Study metric approaches the ideal (trace-condition) limit, highlighting the important role of quantum geometry in the stability of fractionalized phases and their collective excitations. The same trend favors the stability of the long-wavelength quadrupolar mode associated with the chiral graviton. Together, these results identify a distinct interplay between fractionalization and quantum geometry, and provide an analytical framework for studies of collective excitations in fractional topological matter.
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BibTeX
@misc{emanuel2026collective,
title = {{Collective Modes of Fractional States Beyond Landau Levels}},
author = {Peleg Emanuel and Yuval Oreg},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03805},
eprint = {2611.03805},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03805},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Collective Modes of Fractional States Beyond Landau Levels
AU - Peleg Emanuel
AU - Yuval Oreg
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03805
UR - https://arxiv.org/abs/2611.03805
AB - Collective modes provide a powerful probe into the properties and stability of topologically ordered and strongly interacting phases of matter, such as fractional quantum Hall states. Yet, the description of fractional-state excitations away from the Landau-level limit remains a formidable challenge. We develop a framework for describing collective excitations in the strong-coupling regime of coupled-wire constructions and show that they emerge as solitons and breathers of effective sine-Gordon theories. This approach provides a systematic route to studying collective modes in a broad class of fractional states. Applied to a coupled-wire construction of the fractional quantum Hall effect, the framework captures key features of the magnetoroton branch. It naturally extends to fractional Chern insulators, demonstrating that magnetoroton-like collective modes persist well beyond the Landau-level limit. We find that the magnetoroton gap increases as the Fubini-Study metric approaches the ideal (trace-condition) limit, highlighting the important role of quantum geometry in the stability of fractionalized phases and their collective excitations. The same trend favors the stability of the long-wavelength quadrupolar mode associated with the chiral graviton. Together, these results identify a distinct interplay between fractionalization and quantum geometry, and provide an analytical framework for studies of collective excitations in fractional topological matter.
ER -