Symmetric Mode Ansatz: Theory of Magnon Collective Modes in Chern Insulators
Abstract
Moiré materials host integer and fractional Chern insulators (FCIs) where time-reversal is broken spontaneously by flat band ferromagnetism. In twisted MoTe2, unlike in quantum Hall, opposite spins carry opposite Chern numbers and realize Ising ferromagnetism with gapped magnon excitations. Clarifying the nature of these collective modes and the origin of the magnon gap is key to understanding the stability of the Chern magnets in these materials. To do so, we develop a generalized single-mode approximation, which we call the symmetric mode ansatz (SyMA), to describe the low-energy magnon spectrum. We find it to be in exceptional agreement with numerical calculations at integer filling, and qualitatively accurate across fractional fillings including FCIs. To explain the accuracy of the SyMA, we present two families of Hubbard models (including the Haldane model and continuum ideal bands) whose collective modes are analytically solvable and for which the SyMA is either exact or an accurate approximation. For a class of these models where SyMA is exact, we prove two-sided bounds on the zero-momentum magnon gap in terms of the Chern number, Berry curvature, and quantum metric, revealing that uniform quantum geometry is sufficient for stabilizing magnetism in Chern bands.
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BibTeX
@misc{goncalves2026symmetric,
title = {{Symmetric Mode Ansatz: Theory of Magnon Collective Modes in Chern Insulators}},
author = {Miguel Gonçalves and Jonah Herzog-Arbeitman and Juan Felipe Mendez-Valderrama and Andreas Feuerpfeil and B. Andrei Bernevig and Nicolas Regnault},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10706},
eprint = {2610.10706},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10706},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Symmetric Mode Ansatz: Theory of Magnon Collective Modes in Chern Insulators
AU - Miguel Gonçalves
AU - Jonah Herzog-Arbeitman
AU - Juan Felipe Mendez-Valderrama
AU - Andreas Feuerpfeil
AU - B. Andrei Bernevig
AU - Nicolas Regnault
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10706
UR - https://arxiv.org/abs/2610.10706
AB - Moiré materials host integer and fractional Chern insulators (FCIs) where time-reversal is broken spontaneously by flat band ferromagnetism. In twisted MoTe2, unlike in quantum Hall, opposite spins carry opposite Chern numbers and realize Ising ferromagnetism with gapped magnon excitations. Clarifying the nature of these collective modes and the origin of the magnon gap is key to understanding the stability of the Chern magnets in these materials. To do so, we develop a generalized single-mode approximation, which we call the symmetric mode ansatz (SyMA), to describe the low-energy magnon spectrum. We find it to be in exceptional agreement with numerical calculations at integer filling, and qualitatively accurate across fractional fillings including FCIs. To explain the accuracy of the SyMA, we present two families of Hubbard models (including the Haldane model and continuum ideal bands) whose collective modes are analytically solvable and for which the SyMA is either exact or an accurate approximation. For a class of these models where SyMA is exact, we prove two-sided bounds on the zero-momentum magnon gap in terms of the Chern number, Berry curvature, and quantum metric, revealing that uniform quantum geometry is sufficient for stabilizing magnetism in Chern bands.
ER -