Shin-Ming Huang

Quantum-State Projectors on Grassmannian: Geometry, Holonomy, and Topology

An isolated group of $k$ bands in an $N$-level quantum system defines a rank-$k$ spectral projector and hence a map into the complex Grassmannian $\mathrm{Gr}(k,N)$. For a smooth gapped Hamiltonian, this projector is globally smooth and periodic even when band topology obstructs a globally smooth periodic, or symmetry-...