  We show that, quite generally, quantum geometry plays a major role in
determining the low-energy physics in strongly correlated lattice models at
fractional band fillings. We identify limits in which the Fubini Study metric
dictates the ground states and show that this is highly relevant for Moir\'e
materials leading to symmetry breaking and interaction driven Fermi liquids.
This phenomenology stems from a remarkable interplay between the quantum
geometry and interactions which is absent in continuum Landau levels but
generically present in lattice models where these terms tend to destabilize
e.g. fractional Chern insulators. We explain this as a consequence of the
fundamental asymmetry between electrons and holes for band projected normal
ordered interactions, as well as from the perspective of a self-consistent
Hartree-Fock calculation. These basic insights about the role of the quantum
metric turn, when dominant, an extremely strongly coupled problem into an
effectively weakly coupled one, and may also serve as a guiding principle for
designing material setups.
