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quant-ph2026
Quantum-State Projectors on Grassmannian: Geometry, Holonomy, and Topology
Shin-Ming Huang
An isolated group of bands in an -level quantum system defines a rank- spectral projector and hence a map into the complex Grassmannian . For a smooth g…
quant-ph2025
A Gauss-Bonnet Theorem for Quantum States: Gauss Curvature and Topology in the Projective Hilbert Space
Shin-Ming Huang
Geometry and topology are fundamental to modern condensed matter physics, but their precise connection in quantum systems remains incompletely understood. Here, we develop an analy…