Symmetry and Quantum Geometry in Bloch Bands
The paper investigates how to choose real-space positions for atomic orbitals in a tight-binding model to minimize quantum geometric quantities like the variance of Berry curvature or the integrated quantum metric. The main finding is that these optimal positions must respect all spatial symmetries inherent in the tight-binding model, including those related to gauge transformations and time-reversal. This implies that ideal band properties are linked to specific symmetry constraints on orbital placement.