Topological phases of non-interacting systems: A general approach based on states
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916600221794304 |
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| author | De Nittis, Giuseppe |
| author_facet | De Nittis, Giuseppe |
| contents | In this work we provide a classification scheme for topological phases of certain systems whose observable algebra is described by a trivial $C^*$-bundles. The classification is based on the study of the homotopy classes of \emph{configurations}, which are maps from a \emph{quantum parameter space} to the space of pure states of a reference \emph{fiber} $C^*$-algebra. Both the quantum parameter space and the fiber algebra are naturally associated with the observable algebra. A list of various examples described in the last section shows that the common classification scheme of non-interacting topological insulators of type A is recovered inside this new formalism. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_03590 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topological phases of non-interacting systems: A general approach based on states De Nittis, Giuseppe Mathematical Physics Mesoscale and Nanoscale Physics Primary: 81R15, Secondary: 46L30, 81P16, 46L80 In this work we provide a classification scheme for topological phases of certain systems whose observable algebra is described by a trivial $C^*$-bundles. The classification is based on the study of the homotopy classes of \emph{configurations}, which are maps from a \emph{quantum parameter space} to the space of pure states of a reference \emph{fiber} $C^*$-algebra. Both the quantum parameter space and the fiber algebra are naturally associated with the observable algebra. A list of various examples described in the last section shows that the common classification scheme of non-interacting topological insulators of type A is recovered inside this new formalism. |
| title | Topological phases of non-interacting systems: A general approach based on states |
| topic | Mathematical Physics Mesoscale and Nanoscale Physics Primary: 81R15, Secondary: 46L30, 81P16, 46L80 |
| url | https://arxiv.org/abs/2502.03590 |