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DOE OSTI · 2975059

Ordering the topological order in the fractional quantum Hall effect

Cheng, Meng [Yale University, New Haven, CT (United States)] (ORCID:0000000176001809)·Musser, Seth [University of Maryland, College Park, MD (United States)] (ORCID:0000000187468113)·Raz, Amir [University of Texas, Austin, TX (United States)] (ORCID:000000019374169X)·Seiberg, Nathan [Institute for Advanced Study, Princeton, NJ (United States)] (ORCID:000000033897046X)·Senthil, T. [Massachusetts Institute of Technology, Cambridge, MA (United States)]
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Abstract

Here, 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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AnyonsFractional quantum Hall effectQuantum Hall effectTopological field theoriesTopological order

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Cheng, Meng [Yale University, New Haven, CT (United States)] (ORCID:0000000176001809), Musser, Seth [University of Maryland, College Park, MD (United States)] (ORCID:0000000187468113), Raz, Amir [University of Texas, Austin, TX (United States)] (ORCID:000000019374169X), Seiberg, Nathan [Institute for Advanced Study, Princeton, NJ (United States)] (ORCID:000000033897046X), Senthil, T. [Massachusetts Institute of Technology, Cambridge, MA (United States)]. 2026-03-03. Ordering the topological order in the fractional quantum Hall effect. https://doi.org/10.1103/7gtq-y9d9

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