Entanglement spectrum of non-Abelian anyons

doi:10.1088/1674-1056/ac280d

中国物理B ›› 2022, Vol. 31 ›› Issue (3): 37302-037302.doi: 10.1088/1674-1056/ac280d

Entanglement spectrum of non-Abelian anyons

Ying-Hai Wu(吴英海)^†

School of Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China

收稿日期:2021-07-24 修回日期:2021-09-13 接受日期:2021-09-18 出版日期:2022-02-22 发布日期:2022-02-24
通讯作者: Ying-Hai Wu E-mail:yinghaiwu88@hust.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11804107). The author thanks Hong-Hao Tu for helpful commments.

Entanglement spectrum of non-Abelian anyons

Ying-Hai Wu(吴英海)^†

School of Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China

Received:2021-07-24 Revised:2021-09-13 Accepted:2021-09-18 Online:2022-02-22 Published:2022-02-24
Contact: Ying-Hai Wu E-mail:yinghaiwu88@hust.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11804107). The author thanks Hong-Hao Tu for helpful commments.

摘要/Abstract

摘要： Non-Abelian anyons can emerge as fractionalized excitations in two-dimensional systems with topological order. One important example is the Moore—Read fractional quantum Hall state. Its quasihole states are zero-energy eigenstates of a parent Hamiltonian, but its quasiparticle states are not. Both of them can be modeled on an equal footing using the bipartite composite fermion method. We study the entanglement spectrum of the cases with two or four non-Abelian anyons. The counting of levels in the entanglement spectrum can be understood using the edge theory of the Moore—Read state, which reflects the topological order of the system. It is shown that the fusion results of two non-Abelian anyons is determined by their distributions in the bipartite construction.

关键词: fractional quantum Hall effect, anyons, entanglement spectrum, topological order

Abstract: Non-Abelian anyons can emerge as fractionalized excitations in two-dimensional systems with topological order. One important example is the Moore—Read fractional quantum Hall state. Its quasihole states are zero-energy eigenstates of a parent Hamiltonian, but its quasiparticle states are not. Both of them can be modeled on an equal footing using the bipartite composite fermion method. We study the entanglement spectrum of the cases with two or four non-Abelian anyons. The counting of levels in the entanglement spectrum can be understood using the edge theory of the Moore—Read state, which reflects the topological order of the system. It is shown that the fusion results of two non-Abelian anyons is determined by their distributions in the bipartite construction.

Key words: fractional quantum Hall effect, anyons, entanglement spectrum, topological order

中图分类号: (Quantum Hall effects)

73.43.-f

71.10.Pm (Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.)) 03.65.Ud (Entanglement and quantum nonlocality) 03.65.Vf (Phases: geometric; dynamic or topological)

Ying-Hai Wu(吴英海). Entanglement spectrum of non-Abelian anyons[J]. 中国物理B, 2022, 31(3): 37302-037302.

Ying-Hai Wu(吴英海). Entanglement spectrum of non-Abelian anyons[J]. Chin. Phys. B, 2022, 31(3): 37302-037302.

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Entanglement spectrum of non-Abelian anyons

Entanglement spectrum of non-Abelian anyons

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