Ordering the topological order in the fractional quantum Hall effect
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.
Fields of Study & Subjects
Quantum and electron transport phenomena
Surface and Thin Film Phenomena
Graphene research and applications
Publication details
- Journal / source
- Physical review. B./Physical review. B
- Publisher
- American Physical Society (APS)
- Volume
- 113
- Issue
- 11
- Publication date
- 16 January 2026
- Language
- EN