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"Anyonic Symmetries and Topological Defects in Abelian Topological Phases: an application to the ADE Classification", Mayukh Nilay Khan, et al., 2014

Reviewed September 5, 2023

Citation: Khan, Mayukh Nilay, Jeffrey CY Teo, and Taylor L. Hughes. "Anyonic symmetries and topological defects in Abelian topological phases: An application to the A D E classification." Physical Review B 90.23 (2014): 235149.

Web: https://arxiv.org/abs/1403.6478

Tags: Abelian-anyons, Defects/boundaries, Quantum-hall-effect

This paper studies a certain class of abelian topological order which obeys an A-D-E classification theorem. One of the most interesting things about Lie algebras is their symmetry group (especially D3), and one of the things you are most interested in about topological phases is their symmetries. This paper ties the knot, and examines the Lie algebra-inherited symmetries of these abelian phases.

This paper is very fractional-quantum-Hall focused, which is nice. A big focus is put on twist defects and their braidings, which by the time of the writing of this paper were already known to exhibit non-abelian statistics.