PoS - Proceedings of Science
Volume 412 - RDP online PhD school and workshop "Aspects of Symmetry" (Regio2021) - Session 5
On the Wilson loops in 2D tight-binding models
T. Supatashvili*, M. Eliashvili and G. Tsitsishvili
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Published on: May 16, 2022
In the following paper we are considering Hamiltonians with multiband structure. In this case the important quantities to characterize topological states are non-Abelian connection matrix, Berry curvature and Wilson loop. We calculated some of the Wilson loops and showed that their set has a group structure and is isomorphic to $\pi_1(T^2)=\mathbb{Z}\times \mathbb{Z}$. It is shown how to get the same results using the facts known in differential geometry.
DOI: https://doi.org/10.22323/1.412.0021
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