Higher Berry Curvature from the Wave Function. I. Schmidt Decomposition and Matrix Product States

Higher Berry curvature (HBC) is the proposed generalization of Berry curvature to infinitely extended systems. Heuristically, HBC captures the flow of local Berry curvature in a system. Here, we provide a simple formula for computing the HBC for extended d=1 systems at the level of wave functions using the Schmidt decomposition. We also find a corresponding formula for matrix product states and show that for translationally invariant matrix product states this gives rise to a quantized invariant. We demonstrate our approach with an exactly solvable model and numerical calculations for generic models using the infinite density matrix renormalization group algorithm.