富对称拓扑相的精确可解模型
Exactly Solvable Models for Symmetry-Enriched Topological Phases
摘要：
基于对称局部幺正变换的等价类的概念，我们构造了一大类玻色子拓扑（SET）相的不动点波函数和精确可解的投影哈密顿量.我们认为，现场酉对称性，我们的建设实现了所有集的异常，只要潜在的拓扑秩序本身可以实现与一个投影投影哈密顿。我们进一步扩展的建设，反酉对称性（如时间反演对称性），镜像反射对称性，并在表面上的三维拓扑相位的保护的拓扑相位异常设置。在数学上，我们的建设自然会导致一个推广的群扩张的酉融合范畴的反酉对称。
英文摘要：
We construct fixed-point wave functions and exactly solvable commuting-projector Hamiltonians for a large class of bosonic symmetry-enriched topological (SET) phases, based on the concept of equivalent classes of symmetric local unitary transformations. We argue that for onsite unitary symmetries, our construction realizes all SETs free of anomaly, as long as the underlying topological order itself can be realized with a commuting-projector Hamiltonian. We further extend the construction to anti-unitary symmetries (e.g. time-reversal symmetry), mirror-reflection symmetries, and to anomalous SETs on the surface of three-dimensional symmetry-protected topological phases. Mathematically, our construction naturally leads to a generalization of group extensions of unitary fusion categories to anti-unitary symmetries.
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