Stacking and the triviality of invertible phases
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914151187611648 |
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| author | Bachmann, Sven Getz, Alan Naaijkens, Pieter Wray, Naomi |
| author_facet | Bachmann, Sven Getz, Alan Naaijkens, Pieter Wray, Naomi |
| contents | We study the superselection sectors of two quantum lattice systems stacked onto each other in the operator algebraic framework. We show in particular that all irreducible sectors of a stacked system are unitarily equivalent to a product of irreducible sectors of the factors. This naturally leads to a faithful functor between the categories for each system and the category of the stacked system. We construct an intermediate `product' category which we then show is equivalent to the stacked system category. As a consequence, the sectors associated with an invertible state are trivial, namely, invertible states support no anyonic quasi-particles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08382 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stacking and the triviality of invertible phases Bachmann, Sven Getz, Alan Naaijkens, Pieter Wray, Naomi Mathematical Physics Strongly Correlated Electrons Operator Algebras Quantum Physics We study the superselection sectors of two quantum lattice systems stacked onto each other in the operator algebraic framework. We show in particular that all irreducible sectors of a stacked system are unitarily equivalent to a product of irreducible sectors of the factors. This naturally leads to a faithful functor between the categories for each system and the category of the stacked system. We construct an intermediate `product' category which we then show is equivalent to the stacked system category. As a consequence, the sectors associated with an invertible state are trivial, namely, invertible states support no anyonic quasi-particles. |
| title | Stacking and the triviality of invertible phases |
| topic | Mathematical Physics Strongly Correlated Electrons Operator Algebras Quantum Physics |
| url | https://arxiv.org/abs/2511.08382 |