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

Abstract

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

arXiv comment9 pages, 2 figures

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Cited by in corpus (7)

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• Charge pumps, boundary modes, and the necessity of unnecessary criticality
• From quantum geometry to non-linear optics and gerbes: Recent advances in topological band theory
• Equivariant Parameter Families of Spin Chains: A Discrete MPS Formulation