Anomalous matrix product operator symmetries and 1D mixed-state phases

• URL: http://arxiv.org/abs/2504.16985v3
• Date: Wed, 17 Sep 2025 20:25:52 GMT
• Title: Anomalous matrix product operator symmetries and 1D mixed-state phases
• Authors: Xiao-Qi Sun,
• Abstract summary: Generalized symmetries have emerged as a powerful organizing principle for exotic quantum phases.<n>We show that generalized symmetries can be used to probe anomalous quantum phases in open quantum systems.
• Score: 0.8883733362171032
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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