Higher Berry Curvature from the Wave Function I: Schmidt Decomposition and Matrix Product States
Strongly Correlated Electrons
2025-04-28 v1 High Energy Physics - Theory
Quantum Physics
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 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
Keywords
Cite
@article{arxiv.2405.05316,
title = {Higher Berry Curvature from the Wave Function I: Schmidt Decomposition and Matrix Product States},
author = {Ophelia Evelyn Sommer and Xueda Wen and Ashvin Vishwanath},
journal= {arXiv preprint arXiv:2405.05316},
year = {2025}
}
Comments
9 pages, 2 figures