U（1）拓扑相的精确可解模型
Exactly solvable models for U(1) symmetry-enriched topological phases
摘要：
我们提出了一个通用的构造交换投影晶格模型的二维和三维拓扑相位丰富的U（1）对称性，有限维希尔伯特空间每个网站。该构造从拓扑相位的交换投影模型开始，并以一致的方式将U（1）电荷装饰到状态空间。我们证明了所有的二维U（1）拓扑相，允许间隙边界而不破坏对称性，可以通过我们的建设实现。我们还构造了一个大类的3D拓扑相位与U（1）对称粒子或环激发分形。
英文摘要：
We propose a general construction of commuting projector lattice models for 2D and 3D topological phases enriched by U(1) symmetry, with finite-dimensional Hilbert space per site. The construction starts from a commuting projector model of the topological phase and decorates U(1) charges to the state space in a consistent manner. We show that all 2D U(1) symmetry-enriched topological phases which allow gapped boundary without breaking symmetry, can be realized through our construction. We also construct a large class of 3D topological phases with U(1) symmetry fractionalized on particles or loop excitations.
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