Quantization of the higher Berry curvature and the higher Thouless pump
Mathematical Physics
2024-05-14 v2 Strongly Correlated Electrons
High Energy Physics - Theory
math.MP
Abstract
We show that for families of 1d lattice systems in an invertible phase, the cohomology class of the higher Berry curvature can be refined to an integral degree-3 class on the parameter space. Similarly, for families of U(1)-invariant 2d lattice systems in an invertible phase, the higher Thouless pump can be refined to an integral degree-2 class on the parameter space. We show that the 2d Thouless pump can be identified with an excess Berry curvature of a flux insertion.
Keywords
Cite
@article{arxiv.2305.06399,
title = {Quantization of the higher Berry curvature and the higher Thouless pump},
author = {Adam Artymowicz and Anton Kapustin and Nikita Sopenko},
journal= {arXiv preprint arXiv:2305.06399},
year = {2024}
}
Comments
v2: typos corrected, exposition improved, examples of families with nonzero higher Berry class and higher Thouless pump added. Version accepted to Comm. Math. Phys