Fig. 1b: Wilson lines and effectively degenerate Bloch bands.* [Reprinted with permission from AAAS ©2016.]
Topology and geometry are essential to our understanding of modern physics, underlying many foundational concepts from high-energy theories, quantum information, and condensed-matter physics. In condensed-matter systems, a wide range of phenomena stem from the geometry of the band eigenstates, which is encoded in the matrix-valued Wilson line for general multiband systems.