实现编织融合2-范畴为(3+1)维混合态拓扑序
Realizing Braided Fusion 2-Categories as (3+1)D Mixed-State Topological Orders
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中文总结 AI 辅助
本文构造(3+1)维混合态拓扑序族，证明每个编织融合2-范畴可由退相干加规范构造实现，并发现携带引力反常的内禀混合态新机制。
中文摘要 AI 辅助
我们在(3+1)维中构造了大规模的混合态拓扑序族，包括内禀混合态拓扑序。我们通过将参数化编织融合2-范畴的数据与刻画混合态拓扑序的强高阶对称性及其反常联系起来，实现了这些理论。我们在此关注玻色子理论，其中包括在线算子谱中允许出现涌现费米子的理论。我们的通用框架在格点上得到了具体体现，我们提出了具体模型，并识别了编织融合2-范畴的数据如何被物理编码。随后，我们将这些数据形式化，并证明每个编织融合2-范畴都源于一个一般构造（退相干后跟随强和弱规范），作为(3+1)维混合态的拓扑算子范畴，其中内禀混合态拓扑序通过存在强高阶对称性来区分，这些对称性的反常无法在任何(3+1)维有能隙基态中实现。值得注意的是，我们展示了(3+1)维具有一种在(2+1)维中没有对应物的新机制：内禀混合态序，其拓扑算子非退化编织，但携带引力反常。
英文摘要
We construct large families of mixed-state topological orders in (3+1)D, including intrinsically mixed-state topological orders. We realize these theories by relating the data parameterizing braided fusion 2-categories to the strong higher-form symmetries and their anomalies that characterize mixed-state topological order. We focus here on bosonic theories, which include theories which admit an emergent fermion in the spectrum of line operators. Our general framework is exemplified on the lattice, where we present concrete models and identify how the data of braided fusion 2-categories are physically encoded. We then formalize this data and show that every braided fusion 2-category arises from a general construction (decoherence followed by strong and weak gauging) as the category of topological operators of a (3+1)D mixed state, with intrinsically mixed-state topological orders distinguished by the presence of strong higher-form symmetries whose anomalies cannot be realized in any (3+1)D gapped ground state. Notably, we show that (3+1)D admits a new mechanism with no (2+1)D counterpart: intrinsically mixed-state order whose topological operators braid non-degenerately, but which carries a gravitational anomaly.
发表机构
- University of Tokyo（东京大学）
- Bard College（巴德学院）
- Institute for Advanced Study（普林斯顿高等研究院）
机构由 AI 辅助整理，请以论文原文为准。
