Realizing Majorana fermion modes in the Kitaev model

doi:10.1088/1674-1056/ac229a

中国物理B ›› 2021, Vol. 30 ›› Issue (11): 117504-117504.doi: 10.1088/1674-1056/ac229a

Realizing Majorana fermion modes in the Kitaev model

Lu Yang(杨露)¹, Jia-Xing Zhang(张佳星)¹, Shuang Liang(梁爽)³, Wei Chen(陈薇)^1,2,†, and Qiang-Hua Wang(王强华)^1,2

1 National Laboratory of Solid State Microstructures and School of Physics, Nanjing University, Nanjing 210093, China;
2 Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China;
3 Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China

收稿日期:2021-07-16 修回日期:2021-08-24 接受日期:2021-09-01 出版日期:2021-10-13 发布日期:2021-10-27
通讯作者: Wei Chen E-mail:chenweiphy@nju.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11974166 and 11574134).

Realizing Majorana fermion modes in the Kitaev model

Lu Yang(杨露)¹, Jia-Xing Zhang(张佳星)¹, Shuang Liang(梁爽)³, Wei Chen(陈薇)^1,2,†, and Qiang-Hua Wang(王强华)^1,2

1 National Laboratory of Solid State Microstructures and School of Physics, Nanjing University, Nanjing 210093, China;
2 Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China;
3 Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China

Received:2021-07-16 Revised:2021-08-24 Accepted:2021-09-01 Online:2021-10-13 Published:2021-10-27
Contact: Wei Chen E-mail:chenweiphy@nju.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11974166 and 11574134).

摘要/Abstract

摘要： We study the possibility to realize a Majorana zero mode that is robust and may be easily manipulated for braiding in quantum computing in the ground state of the Kitaev model in this work. To achieve this we first apply a uniform [111] magnetic field to the gapless Kitaev model and turn the Kitaev model to an effective p+ip topological superconductor of spinons. We then study possible vortex binding in such system to a topologically trivial spot in the ground state. We consider two cases in the system: one is a vacancy and the other is a fully polarized spin. We show that in both cases, the system binds a vortex with the defect and a robust Majorana zero mode in the ground state at a weak uniform [111] magnetic field. The distribution and asymptotic behavior of these Majorana zero modes are studied. The Majorana zero modes in both cases decay exponentially in space, and are robust against local perturbations and other Majorana zero modes far away, which makes them promising candidates for braiding in topological quantum computing.

关键词: Kitaev model, Majorana fermion modes, topological quantum computing

Abstract: We study the possibility to realize a Majorana zero mode that is robust and may be easily manipulated for braiding in quantum computing in the ground state of the Kitaev model in this work. To achieve this we first apply a uniform [111] magnetic field to the gapless Kitaev model and turn the Kitaev model to an effective p+ip topological superconductor of spinons. We then study possible vortex binding in such system to a topologically trivial spot in the ground state. We consider two cases in the system: one is a vacancy and the other is a fully polarized spin. We show that in both cases, the system binds a vortex with the defect and a robust Majorana zero mode in the ground state at a weak uniform [111] magnetic field. The distribution and asymptotic behavior of these Majorana zero modes are studied. The Majorana zero modes in both cases decay exponentially in space, and are robust against local perturbations and other Majorana zero modes far away, which makes them promising candidates for braiding in topological quantum computing.

Key words: Kitaev model, Majorana fermion modes, topological quantum computing

中图分类号: (Quantum spin liquids, valence bond phases and related phenomena)

75.10.Kt

75.10.Hk (Classical spin models)

Lu Yang(杨露), Jia-Xing Zhang(张佳星), Shuang Liang(梁爽), Wei Chen(陈薇), and Qiang-Hua Wang(王强华). Realizing Majorana fermion modes in the Kitaev model[J]. 中国物理B, 2021, 30(11): 117504-117504.

Lu Yang(杨露), Jia-Xing Zhang(张佳星), Shuang Liang(梁爽), Wei Chen(陈薇), and Qiang-Hua Wang(王强华). Realizing Majorana fermion modes in the Kitaev model[J]. Chin. Phys. B, 2021, 30(11): 117504-117504.

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Realizing Majorana fermion modes in the Kitaev model

Realizing Majorana fermion modes in the Kitaev model

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