Electric-magnetic duality in twisted quantum double model of topological orders

Journal of High Energy Physics

Yuting Hu¹  Yidun Wan² 

[1] Department of Physics and Institute for Quantum Science and Engineering, South University of Science and Technology, 1088 Xueyuan Ave, Nanshan, Shenzhen, China;State Key Laboratory of Surface Physics, Fudan University, 220 Handan Rd, Yangpu District, Shanghai, China;eCAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern Physics, University of Science and Technology of China, No. 96 Rd, Hefei, China;State Key Laboratory of Surface Physics, Fudan University, 220 Handan Rd, Yangpu District, Shanghai, China;Department of Physics, Center for Field Theory and Particle Physics, and Institute for Nanoelectronic devices and Quantum computing, Fudan University, 220 Handan Rd, Yangpu District, Shanghai, China;Department of Physics and Institute for Quantum Science and Engineering, South University of Science and Technology, 1088 Xueyuan Ave, Nanshan, Shenzhen, China;

关键词: Topological States of Matter;    Anyons;    Duality in Gauge Field Theories;   

DOI  :  10.1007/JHEP11(2020)170

来源: Springer

【 摘 要 】

We derive a partial electric-magnetic (PEM) duality transformation of the twisted quantum double (TQD) model TQD(G, α) — discrete Dijkgraaf-Witten model — with a finite gauge group G, which has an Abelian normal subgroup N , and a three-cocycle α ∈ H3(G, U(1)). Any equivalence between two TQD models, say, TQD(G, α) and TQD(G′, α′), can be realized as a PEM duality transformation, which exchanges the N-charges and N-fluxes only. Via the PEM duality, we construct an explicit isomorphism between the corresponding TQD algebras Dα(G) and Dα′(G′) and derive the map between the anyons of one model and those of the other.

【 授权许可】

CC BY