Non-Abelian Quantum Metric Governed Topological Boundary-Mode Localization
This research investigates how localized boundary modes in topological flat-band systems are spatially constrained by a quantum metric length (QML). The study shows that QML, derived from the non-Abelian quantum metric of degenerate flat bands, sets a fundamental lower bound on the spatial spread of these boundary states. This geometric constraint governs long-range behavior and dictates observable phenomena like anomalous Hall plateaus.