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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.15168 |
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| _version_ | 1866911597089259520 |
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| author | Gunn, David Styliaris, Georgios Kraus, Barbara Kraft, Tristan |
| author_facet | Gunn, David Styliaris, Georgios Kraus, Barbara Kraft, Tristan |
| contents | We study phases of one-dimensional matrix-product states (MPS) when transformations are restricted to symmetric local circuits supplemented with symmetric measurements and feedforward (G-CMF). Building on the framework introduced in Gunn et al., Phys. Rev. B 111, 115110 (2025), we extend the analysis to all finite nilpotent groups for which we obtain a complete classification of G-CMF phases. We construct explicit symmetry-respecting protocols that map any symmetry-protected topological (SPT) or non-normal (GHZ-type) MPS to the trivial phase-and vice versa-with success probability approaching one in the thermodynamic limit. The key technical ingredient is a finite hierarchical structure of irreducible representations of nilpotent groups, which enables successive rounds of symmetric measurements to systematically reduce non-abelian components to abelian ones. Our results demonstrate that allowing symmetric measurements and feedforward fundamentally simplifies the phase structure of 1D systems with nilpotent symmetries: all SPT and non-normal MPS phases collapse into a single asymptotically equivalent phase under G-CMF transformations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_15168 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Phases of matrix-product states with symmetries and measurements: Finite nilpotent groups Gunn, David Styliaris, Georgios Kraus, Barbara Kraft, Tristan Quantum Physics We study phases of one-dimensional matrix-product states (MPS) when transformations are restricted to symmetric local circuits supplemented with symmetric measurements and feedforward (G-CMF). Building on the framework introduced in Gunn et al., Phys. Rev. B 111, 115110 (2025), we extend the analysis to all finite nilpotent groups for which we obtain a complete classification of G-CMF phases. We construct explicit symmetry-respecting protocols that map any symmetry-protected topological (SPT) or non-normal (GHZ-type) MPS to the trivial phase-and vice versa-with success probability approaching one in the thermodynamic limit. The key technical ingredient is a finite hierarchical structure of irreducible representations of nilpotent groups, which enables successive rounds of symmetric measurements to systematically reduce non-abelian components to abelian ones. Our results demonstrate that allowing symmetric measurements and feedforward fundamentally simplifies the phase structure of 1D systems with nilpotent symmetries: all SPT and non-normal MPS phases collapse into a single asymptotically equivalent phase under G-CMF transformations. |
| title | Phases of matrix-product states with symmetries and measurements: Finite nilpotent groups |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2602.15168 |