Non-Abelian three-loop braiding statistics for 3D fermionic topological phases

Jing-Ren Zhou, Qing-Rui Wang, Chenjie Wang () and Zheng-Cheng Gu ()
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Jing-Ren Zhou: The Chinese University of Hong Kong
Qing-Rui Wang: The Chinese University of Hong Kong
Chenjie Wang: The University of Hong Kong
Zheng-Cheng Gu: The Chinese University of Hong Kong

Nature Communications, 2021, vol. 12, issue 1, 1-10

Abstract: Abstract Fractional statistics is one of the most intriguing features of topological phases in 2D. In particular, the so-called non-Abelian statistics plays a crucial role towards realizing topological quantum computation. Recently, the study of topological phases has been extended to 3D and it has been proposed that loop-like extensive objects can also carry fractional statistics. In this work, we systematically study the so-called three-loop braiding statistics for 3D interacting fermion systems. Most surprisingly, we discover new types of non-Abelian three-loop braiding statistics that can only be realized in fermionic systems (or equivalently bosonic systems with emergent fermionic particles). On the other hand, due to the correspondence between gauge theories with fermionic particles and classifying fermionic symmetry-protected topological (FSPT) phases with unitary symmetries, our study also gives rise to an alternative way to classify FSPT phases. We further compare the classification results for FSPT phases with arbitrary Abelian unitary total symmetry Gf and find systematical agreement with previous studies.

Date: 2021
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DOI: 10.1038/s41467-021-23309-3

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