Exploring Grassmann manifolds in topological systems via quantum distance
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909874277842944 |
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| author | Huang, Shin-Ming Giataganas, Dimitrios |
| author_facet | Huang, Shin-Ming Giataganas, Dimitrios |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20046 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exploring Grassmann manifolds in topological systems via quantum distance Huang, Shin-Ming Giataganas, Dimitrios Mesoscale and Nanoscale Physics Quantum Physics 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. |
| title | Exploring Grassmann manifolds in topological systems via quantum distance |
| topic | Mesoscale and Nanoscale Physics Quantum Physics |
| url | https://arxiv.org/abs/2412.20046 |