We construct a class of 2+1 dimensional relativistic quantum field theories which exhibit the fractional quantum Hall effect in the infrared, both in the continuum and on the lattice. The UV completion consists of a perturbative U(1)×U(1) gauge theory with integer-charged fields, while the low energy spectrum consists of nontrivial topological phases supporting fractional currents, bulk anyonic excitations, and exotic phenomena such as a fractional quantum spin Hall effect. We show explicitly how fractionally charged chiral edge states emerge in the IR.

中文翻译：

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相对论场论中的分数量子霍尔效应。

我们构建了一类2 + 1维相对论量子场论，它们在红外光中在连续谱和晶格中均表现出分数量子霍尔效应。紫外线完成包括具有整数电荷场的摄动U（1）×U（1）规范理论，而低能谱则由支持分数流，本体非调子激发和奇异现象（例如分数量子）的非平凡拓扑相组成。旋转霍尔效应。我们明确显示了红外中如何出现部分带电的手性边缘态。