Quantum Geometry Driven Fluctuation Phenomena in Flat-Band Systems

Quantum geometry plays a fundamental role in shaping emergent phases in flat-band systems. Here, we discuss collective excitonic phenomena in quantum-geometry-induced flat bands, highlighting how the quantum metric influences both the condensation and fluctuation dynamics. We identify a novel state involving finite-momentum fluctuations linked to the underlying quantum geometry, which should be experimentally accessible via its magnetic responses. Our study points to a broader framework in which quantum geometry governs many-body behavior in engineered quantum materials.