Classification of topological phases with finite internal symmetries in all dimensions

Journal of High Energy Physics

Xiao-Gang Wen¹  Tian Lan²  Zhi-Hao Zhang³  Liang Kong⁴  Hao Zheng⁵ 

[1] Department of Physics, Massachusetts Institute of Technology, 02139, Cambridge, MA, USA;Institute for Quantum Computing, University of Waterloo, N2L 3G1, Waterloo, ON, Canada;School of Mathematical Sciences, University of Science and Technology of China, 230026, Hefei, China;Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, 518055, Shenzhen, China;Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, 518055, Shenzhen, China;Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, 518055, Shenzhen, China;Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, 518055, Shenzhen, China;Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, 518055, Shenzhen, China;Department of Mathematics, Peking University, 100871, Beijing, China;

关键词: Topological States of Matter;    Anomalies in Field and String Theories;    Anyons;    Gauge Symmetry;   

DOI  :  10.1007/JHEP09(2020)093

来源: Springer

【 摘 要 】

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.

【 授权许可】

CC BY