The Symmetry Taco: Equivalences between Gapped, Gapless, and Mixed-State SPTs
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909819822145536 |
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| author | Qi, Marvin Sohal, Ramanjit Chen, Xie Stephen, David T. Prem, Abhinav |
| author_facet | Qi, Marvin Sohal, Ramanjit Chen, Xie Stephen, David T. Prem, Abhinav |
| contents | Symmetry topological field theory (SymTFT), or topological holography, offers a unifying framework for describing quantum phases of matter and phase transitions between them. While this approach has seen remarkable success in describing gapped and gapless pure-state phases in $1+1$d, its applicability to open quantum systems remains entirely unexplored. In this work, we propose a natural extension of the SymTFT framework to mixed-state phases by introducing the \textit{symmetry taco}: a bilayer topological order in $2+1$d whose folded geometry naturally encapsulates both strong and weak symmetries of the $1+1$d theory. We use this perspective to identify a series of correspondences, including a one-to-one map between intrinsically gapless SPTs (igSPTs) and certain gapped SPTs, and a mapping between igSPTs and intrinsically average SPTs (iASPTs) arising in $1+1$d mixed states. More broadly, our framework yields a classification of short-range correlated $G$-symmetric Choi states in $1+1$d, provides a route for systematically generating mixed-state SPTs via local decoherence of igSPTs, and allows us to identify a new mixed-state ``anomaly". Besides folding in mixed-state phases into the SymTFT paradigm, the symmetry taco opens new avenues for exploring dualities, anomalies, and non-equilibrium criticality in mixed-state quantum matter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_05335 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Symmetry Taco: Equivalences between Gapped, Gapless, and Mixed-State SPTs Qi, Marvin Sohal, Ramanjit Chen, Xie Stephen, David T. Prem, Abhinav Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics Symmetry topological field theory (SymTFT), or topological holography, offers a unifying framework for describing quantum phases of matter and phase transitions between them. While this approach has seen remarkable success in describing gapped and gapless pure-state phases in $1+1$d, its applicability to open quantum systems remains entirely unexplored. In this work, we propose a natural extension of the SymTFT framework to mixed-state phases by introducing the \textit{symmetry taco}: a bilayer topological order in $2+1$d whose folded geometry naturally encapsulates both strong and weak symmetries of the $1+1$d theory. We use this perspective to identify a series of correspondences, including a one-to-one map between intrinsically gapless SPTs (igSPTs) and certain gapped SPTs, and a mapping between igSPTs and intrinsically average SPTs (iASPTs) arising in $1+1$d mixed states. More broadly, our framework yields a classification of short-range correlated $G$-symmetric Choi states in $1+1$d, provides a route for systematically generating mixed-state SPTs via local decoherence of igSPTs, and allows us to identify a new mixed-state ``anomaly". Besides folding in mixed-state phases into the SymTFT paradigm, the symmetry taco opens new avenues for exploring dualities, anomalies, and non-equilibrium criticality in mixed-state quantum matter. |
| title | The Symmetry Taco: Equivalences between Gapped, Gapless, and Mixed-State SPTs |
| topic | Strongly Correlated Electrons High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2507.05335 |