Classification of topological phases with finite internal symmetries in all dimensions

Kong，Liang1,2; Lan，Tian3; Wen，Xiao Gang4; Zhang，Zhi Hao1,5; Zheng，Hao1,2,6

2020-09-01

10.1007/JHEP09(2020)093

Journal of High Energy Physics   影响因子和分区

1029-8479

1029-8479

We develop a mathematical theory of symmetry protected trivial (SPT) orders and anomaly-free symmetry enriched topological (SET) orders in all dimensions via two different approaches with an emphasis on the second approach. The first approach is to gauge the symmetry in the same dimension by adding topological excitations as it was done in the 2d case, in which the gauging process is mathematically described by the minimal modular extensions of unitary braided fusion 1-categories. This 2d result immediately generalizes to all dimensions except in 1d, which is treated with special care. The second approach is to use the 1-dimensional higher bulk of the SPT/SET order and the boundary-bulk relation. This approach also leads us to a precise mathematical description and a classification of SPT/SET orders in all dimensions. The equivalence of these two approaches, together with known physical results, provides us with many precise mathematical predictions.

Anomalies in Field and String Theories Anyons Gauge Symmetry Topological States of Matter

SCI

英语

第一

Guangdong Provincial Key Laboratory[2019B121203002] ; NSFC[11971219][11871078] ; NSF[DMS-1664412] ; Simons Collaboration on UltraQuantum Matter from the Simons Foundation[651440]

Physics

Physics, Particles & Fields

WOS:000573285600002

SPRINGER

PHYSICS

2-s2.0-85090935401

Scopus

1.Shenzhen Institute for Quantum Science and Engineering,Southern University of Science and Technology,Shenzhen,518055,China
2.Guangdong Provincial Key Laboratory of Quantum Science and Engineering,Southern University of Science and Technology,Shenzhen,518055,China
3.Institute for Quantum Computing,University of Waterloo,Waterloo,N2L 3G1,Canada
4.Department of Physics,Massachusetts Institute of Technology,Cambridge,02139,United States
5.School of Mathematical Sciences,University of Science and Technology of China,Hefei,230026,China
6.Department of Mathematics,Peking University,Beijing,100871,China

Kong，Liang,Lan，Tian,Wen，Xiao Gang,et al. Classification of topological phases with finite internal symmetries in all dimensions[J]. Journal of High Energy Physics,2020,2020(9).

Kong，Liang,Lan，Tian,Wen，Xiao Gang,Zhang，Zhi Hao,&Zheng，Hao.(2020).Classification of topological phases with finite internal symmetries in all dimensions.Journal of High Energy Physics,2020(9).

Kong，Liang,et al."Classification of topological phases with finite internal symmetries in all dimensions".Journal of High Energy Physics 2020.9(2020).