Band-resolved automatic differentiation method for first-principles quantum response calculations

The accurate calculation of Bloch state derivatives is numerically challenging yet indispensable for evaluating the quantum response functions, such as how materials interact with light. Here, the authors develop a band-resolved automatic differentiation approach for efficiently calculating quantum response properties, eliminating the need for manual analytical derivations and time-consuming full-band summation. This work incorporates the quantum response calculation into a broader paradigm of differentiable programming, unlocking new pathways for data-driven exploration and design of advanced quantum materials.