Exploring Grassmann manifolds in topological systems via quantum distance

• URL: http://arxiv.org/abs/2412.20046v2
• Date: Wed, 29 Oct 2025 07:05:20 GMT
• Title: Exploring Grassmann manifolds in topological systems via quantum distance
• Authors: Shin-Ming Huang, Dimitrios Giataganas,
• Abstract summary: Quantum states defined over a parameter space form a Grassmann manifold.<n>We employ the projector of a multilevel system to quantify the quantum distance between states.<n>Using the multidimensional scaling method, we transform the quantum distance into a reconstructed manifold embedded in Euclidean space.
• Score: 0.0
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: Quantum states defined over a parameter space form a Grassmann manifold. To capture the geometry of the associated gauge structure, gauge-invariant quantities are essential. We employ the projector of a multilevel system to quantify the quantum distance between states. Using the multidimensional scaling method, we transform the quantum distance into a reconstructed manifold embedded in Euclidean space. This approach is demonstrated with examples of topological systems, showcasing their topological features within these manifolds. Our method provides a comprehensive view of the manifold, rather than focusing on local properties.

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