Anyonic exclusions statistics on surfaces with gapped boundaries

Li, Yingcheng1,2,3; Wang, Hongyu1,2,3; Hu, Yuting4,6,7; Wan, Yidun1,2,3,4,5,6,7,8

2019-04-09

10.1007/JHEP04(2019)078

JOURNAL OF HIGH ENERGY PHYSICS   影响因子和分区

1029-8479

An anyonic exclusion statistics, which generalizes the Bose-Einstein and Fermi-Dirac statistics of bosons and fermions, was proposed by Haldane [1]. When fusion of anyons is involved, certain 'pseudo-species' anyons appear in the exotic statistical weights of non-Abelian anyon systems; however, the meaning and significance of pseudo-species remains an open problem. The relevant past studies had considered only anyon systems without any physical boundary but boundaries often appear in real-life materials. In this paper, we propose an extended anyonic exclusion statistics on surfaces with gapped boundaries, introducing mutual exclusion statistics between anyons as well as the boundary components. Motivated by refs. [2, 3], we present a formula for the statistical weight of many-anyon states obeying the proposed statistics. Taking the (doubled) Fibonacci topological order as an example, we develop a systematic basis construction for non-Abelian anyons on any Riemann surfaces with gapped boundaries. The basis construction offers a standard way to read off a canonical set of statistics parameters and hence write down the extended statistical weight of the anyon system being studied. The basis construction reveals the meaning of pseudo-species. A pseudo-species has different 'excitation' modes, each corresponding to an anyon species. The 'excitation' modes of pseudo-species corresponds to good quantum numbers of subsystems of a non-Abelian anyon system. This is important because often (e.g., in topological quantum computing) we may be concerned about only the entanglement between such subsystems.

Anyons Topological Field Theories Topological States of Matter

SCI

英语

通讯

Shanghai Pujiang Program[KBH1512328]

Physics

Physics, Particles & Fields

WOS:000464734300011

SPRINGER

PHYSICS

Web of Science

1.Fudan Univ, State Key Lab Surface Phys, Shanghai 200433, Peoples R China
2.Fudan Univ, Dept Phys, Shanghai 200433, Peoples R China
3.Fudan Univ, Ctr Field Theory & Particle Phys, Shanghai 200433, Peoples R China
4.Ctr Quantum Comp, Peng Cheng Lab, Shenzhen 518055, Peoples R China
5.Fudan Univ, Inst Nanoelect Devices & Quantum Comp, Shanghai 200433, Peoples R China
6.Southern Univ Sci & Technol, Dept Phys, Shenzhen 518055, Peoples R China
7.Southern Univ Sci & Technol, Inst Quantum Sci & Engn, Shenzhen 518055, Peoples R China
8.Collaborat Innovat Ctr Adv Microstruct, Nanjing 210093, Jiangsu, Peoples R China

Li, Yingcheng,Wang, Hongyu,Hu, Yuting,et al. Anyonic exclusions statistics on surfaces with gapped boundaries[J]. JOURNAL OF HIGH ENERGY PHYSICS,2019(4).

Li, Yingcheng,Wang, Hongyu,Hu, Yuting,&Wan, Yidun.(2019).Anyonic exclusions statistics on surfaces with gapped boundaries.JOURNAL OF HIGH ENERGY PHYSICS(4).

Li, Yingcheng,et al."Anyonic exclusions statistics on surfaces with gapped boundaries".JOURNAL OF HIGH ENERGY PHYSICS .4(2019).