Quantum

Realizing Braided Fusion 2-Categories as (3+1)D Mixed-State Topological Orders

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Briefings

The paper constructs large families of mixed-state topological orders in (3+1)D by relating braided fusion 2-category data to strong higher-form symmetries and their anomalies. It focuses on bosonic theories with emergent fermions and presents concrete lattice models. The authors formalize this data, showing every braided fusion 2-category arises from decoherence, strong, and weak gauging. Intrinsically mixed-state orders are distinguished by strong higher-form symmetries whose anomalies cannot be realized in (3+1)D gapped ground states. A new mechanism is identified where topological operators braid non-degenerately while carrying a gravitational anomaly, which has no (2+1)D counterpart.

Key points

• The paper constructs large families of mixed-state topological orders in (3+1)D by relating braided fusion 2-category data to strong higher-form symmetries and their anomalies.
• Intrinsically mixed-state orders are distinguished by strong higher-form symmetries whose anomalies cannot be realized in any (3+1)D gapped ground state.

Context and limitations

The study focuses on bosonic theories and presents concrete lattice models; it does not provide exhaustive data for all possible (3+1)D mixed-state orders.

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