Group structure of Wilson loops in 2D tight-binding models with 2-band and 4-band energy spectra

Tight-binding models represent one of the basic approaches for studying topological states a matter. In given account, we consider tight-binding model set by matrix Hamiltonian over 2D Brillouin zone. The corresponding multiband energy spectrum gives rise to non-Abelian gauge construction formed Berry connection [Formula: see text]. main invariant quantities in such cases are eigenvalues Wilson loops. purpose followed is search any special (on top general) properties loops which impose certain restrictions on structure its eigenvalues. shown be pure with point-like singularities. curvature tensor text] vanishes throughout zone except isolated points where singular. Combining behavior Stokes theorem allows avoid path-ordering procedure calculating this approach, show that endowed group isomorphic fundamental latter Abelian forcing comprise two fixed phases associated primitive elements (generators)