The Lieb-Robinson condition and the Fréchet topology
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909939698499584 |
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| author | Bachmann, Sven De Nittis, Giuseppe Gómez, Julián |
| author_facet | Bachmann, Sven De Nittis, Giuseppe Gómez, Julián |
| contents | We define various notions of locality for *-automorphisms of the algebra of observables for an infinitely extended quantum spin system and study their relationship. In particular, we show that the ubiquitous characterization which arises from the Lieb-Robinson bound implies but is not equivalent to continuity with respect to the natural Fréchet topology of almost local observables, which is a non-commutative analog of the Schwartz space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_02181 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Lieb-Robinson condition and the Fréchet topology Bachmann, Sven De Nittis, Giuseppe Gómez, Julián Mathematical Physics Primary: 81R15, Secondary: 46N50, 46A04 We define various notions of locality for *-automorphisms of the algebra of observables for an infinitely extended quantum spin system and study their relationship. In particular, we show that the ubiquitous characterization which arises from the Lieb-Robinson bound implies but is not equivalent to continuity with respect to the natural Fréchet topology of almost local observables, which is a non-commutative analog of the Schwartz space. |
| title | The Lieb-Robinson condition and the Fréchet topology |
| topic | Mathematical Physics Primary: 81R15, Secondary: 46N50, 46A04 |
| url | https://arxiv.org/abs/2512.02181 |