Higher Berry Curvature from the Wave Function I: Schmidt Decomposition and Matrix Product States
arxiv(2024)
摘要
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 (MPS), and show that for translationally invariant MPS
this gives rise to a quantized invariant. We demonstrate our approach with an
exactly solvable model and numerical calculations for generic models using
iDMRG
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