Anomalous matrix product operator symmetries and 1D mixed-state phases
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909793908686848 |
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| author | Sun, Xiao-Qi |
| author_facet | Sun, Xiao-Qi |
| contents | Generalized symmetries have emerged as a powerful organizing principle for exotic quantum phases. However, their role in open quantum systems, especially for non-invertible cases, remains largely unexplored. We address this by applying a unified tensor-network framework for mixed states with fusion categorical symmetry, which encompasses both invertible and non-invertible ones represented as matrix product operators, and reveals novel quantum phases unique to the open-system setting through the lens of quantum anomalies. In contrast to pure states, where anomalies forbid symmetric short-range correlated phases in one dimension, we construct a broad class of renormalization fixed-point mixed states with zero correlation length given arbitrary strong anomalous fusion categorical symmetry. These states, representing nontrivial mixed-state phases of matter, cannot be efficient prepared via local quantum channels, indicating anomaly-enforced long-range entanglement in the absence of local correlations. Despite this obstruction, we further provide constructions of measurement-enhanced quantum circuits to prepare all these constructed states, offering a practical way to realize and probe anomalous generalized symmetries in open quantum systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16985 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Anomalous matrix product operator symmetries and 1D mixed-state phases Sun, Xiao-Qi Quantum Physics Strongly Correlated Electrons Generalized symmetries have emerged as a powerful organizing principle for exotic quantum phases. However, their role in open quantum systems, especially for non-invertible cases, remains largely unexplored. We address this by applying a unified tensor-network framework for mixed states with fusion categorical symmetry, which encompasses both invertible and non-invertible ones represented as matrix product operators, and reveals novel quantum phases unique to the open-system setting through the lens of quantum anomalies. In contrast to pure states, where anomalies forbid symmetric short-range correlated phases in one dimension, we construct a broad class of renormalization fixed-point mixed states with zero correlation length given arbitrary strong anomalous fusion categorical symmetry. These states, representing nontrivial mixed-state phases of matter, cannot be efficient prepared via local quantum channels, indicating anomaly-enforced long-range entanglement in the absence of local correlations. Despite this obstruction, we further provide constructions of measurement-enhanced quantum circuits to prepare all these constructed states, offering a practical way to realize and probe anomalous generalized symmetries in open quantum systems. |
| title | Anomalous matrix product operator symmetries and 1D mixed-state phases |
| topic | Quantum Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2504.16985 |