Selecting orbitals for effective models using quantum geometry

Develop principled criteria and algorithms to identify the minimal set of orbitals needed in effective low-energy models of multi-orbital materials and incorporate quantum-geometric corrections—encoded by the quantum geometric tensor and the dipole-fluctuation length scale ℓ_g—so that the resulting truncated Hilbert space faithfully captures inter-orbital mixing and its impact on observables.

Background

The review emphasizes that quantum geometry quantifies corrections arising from orbital mixing when truncating the Hilbert space in effective theories. Determining which orbitals must be retained is a key modeling decision that affects the accuracy of predictions for transport and collective phenomena.

A systematic, geometry-aware selection of orbitals would enable minimal models that preserve the relevant dipole fluctuations and interband mixing, avoiding reliance on the full atomic basis while maintaining predictive power.