Collective Modes of Fractional States Beyond Landau Levels

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.