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arXiv · 2505.14767

Ordering the topological order in the fractional quantum Hall effect

Meng Cheng·Seth Musser·Amir Raz·Nathan Seiberg·T. Senthil
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Abstract

We discuss the possible topological order/topological quantum field theory of different quantum Hall systems. Given the value of the Hall conductivity, we constrain the global symmetry of the low-energy theory and its anomaly. Specifically, the one-form global symmetry and its anomaly are presented as the organizing principle of these systems. This information is powerful enough to lead to a unique minimal topological order (or a small number of minimal topological orders). Almost all of the known experimentally discovered topological orders are these minimal theories. Since this work is interdisciplinary, we made a special effort to relate to researchers with different backgrounds by providing translations between different perspectives.

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Meng Cheng, Seth Musser, Amir Raz, Nathan Seiberg, T. Senthil. 2025-05-20. Ordering the topological order in the fractional quantum Hall effect. https://doi.org/10.1103/7gtq-y9d9

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