Fubini-Study metric tensor and quantum geometric tensor of Bloch bands
The quantum geometric tensor Q_{μν}(k) = <∂_μu|∂_νu> - <∂_μu|u><u|∂_νu> contains the Berry curvature Ω (imaginary part, related to Hall conductance) and the quantum metric g (real part). The metric measures state distinguishability in k-space and bounds superfluid weight and spread of Wannier functions.