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arXiv · 2405.05316

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

Ophelia Evelyn Sommer·Xueda Wen·Ashvin Vishwanath
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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

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Ophelia Evelyn Sommer, Xueda Wen, Ashvin Vishwanath. 2024-05-08. Higher Berry Curvature from the Wave Function I: Schmidt Decomposition and Matrix Product States. https://doi.org/10.1103/physrevlett.134.146601

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