Classifying symmetric and symmetry-broken spin chain phases with anomalous group actions
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910386630950912 |
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| author | Rubio, Jose Garre Molnar, Andras Ogata, Yoshiko |
| author_facet | Rubio, Jose Garre Molnar, Andras Ogata, Yoshiko |
| contents | We consider the classification problem of quantum spin chains invariant under local decomposable group actions, covering matrix product unitaries (MPUs), using an operator algebraic approach. We focus on finite group symmetries hosting both symmetric and symmetry broken phases. The local-decomposable group actions we consider have a 3-cocycle class of the symmetry group associated to them. We derive invariants for our classification that naturally cover one-dimensional symmetry protected topological (SPT) phases. We prove that these invariants coincide with the ones of [J. Garre Rubio et al, Quantum 7, 927 (2023)] using matrix product states (MPSs) techniques, by explicitly working out the GNS representation of MPSs and MPUs, resulting in a useful dictionary between both approaches that could be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18573 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classifying symmetric and symmetry-broken spin chain phases with anomalous group actions Rubio, Jose Garre Molnar, Andras Ogata, Yoshiko Quantum Physics Mathematical Physics We consider the classification problem of quantum spin chains invariant under local decomposable group actions, covering matrix product unitaries (MPUs), using an operator algebraic approach. We focus on finite group symmetries hosting both symmetric and symmetry broken phases. The local-decomposable group actions we consider have a 3-cocycle class of the symmetry group associated to them. We derive invariants for our classification that naturally cover one-dimensional symmetry protected topological (SPT) phases. We prove that these invariants coincide with the ones of [J. Garre Rubio et al, Quantum 7, 927 (2023)] using matrix product states (MPSs) techniques, by explicitly working out the GNS representation of MPSs and MPUs, resulting in a useful dictionary between both approaches that could be of independent interest. |
| title | Classifying symmetric and symmetry-broken spin chain phases with anomalous group actions |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2403.18573 |