High winding number of topological phase in non-unitary periodic quantum walk

doi:10.1088/1674-1056/abf554

中国物理B ›› 2021, Vol. 30 ›› Issue (10): 100301-100301.doi: 10.1088/1674-1056/abf554

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High winding number of topological phase in non-unitary periodic quantum walk

Yali Jia(贾雅利) and Zhi-Jian Li(李志坚)^†

Institute of Theoretical Physics, Shanxi University, Taiyuan 030006, China

收稿日期:2021-01-07 修回日期:2021-03-10 接受日期:2021-04-07 出版日期:2021-09-17 发布日期:2021-09-17
通讯作者: Zhi-Jian Li E-mail:zjli@sxu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 12004231).

High winding number of topological phase in non-unitary periodic quantum walk

Yali Jia(贾雅利) and Zhi-Jian Li(李志坚)^†

Institute of Theoretical Physics, Shanxi University, Taiyuan 030006, China

Received:2021-01-07 Revised:2021-03-10 Accepted:2021-04-07 Online:2021-09-17 Published:2021-09-17
Contact: Zhi-Jian Li E-mail:zjli@sxu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 12004231).

摘要/Abstract

摘要： Topological phases and their associated multiple edge states are studied by constructing a one-dimensional non-unitary multi-period quantum walk with parity-time symmetry. It is shown that large topological numbers can be obtained when choosing an appropriate time frame. The maximum value of the winding number can reach the number of periods in the one-step evolution operator. The validity of the bulk-edge correspondence is confirmed, while for an odd-period quantum walk and an even-period quantum walk, they have different configurations of the 0-energy edge state and π-energy edge state. On the boundary, two kinds of edge states always coexist in equal amount for the odd-period quantum walk, however three cases including equal amount, unequal amount or even only one type may occur for the even-period quantum walk.

关键词: periodic quantum walk, high winding number, edge states

Abstract: Topological phases and their associated multiple edge states are studied by constructing a one-dimensional non-unitary multi-period quantum walk with parity-time symmetry. It is shown that large topological numbers can be obtained when choosing an appropriate time frame. The maximum value of the winding number can reach the number of periods in the one-step evolution operator. The validity of the bulk-edge correspondence is confirmed, while for an odd-period quantum walk and an even-period quantum walk, they have different configurations of the 0-energy edge state and π-energy edge state. On the boundary, two kinds of edge states always coexist in equal amount for the odd-period quantum walk, however three cases including equal amount, unequal amount or even only one type may occur for the even-period quantum walk.

Key words: periodic quantum walk, high winding number, edge states

中图分类号: (Quantum algorithms, protocols, and simulations)

03.67.Ac

05.40.Fb (Random walks and Levy flights) 03.65.Vf (Phases: geometric; dynamic or topological)

Yali Jia(贾雅利) and Zhi-Jian Li(李志坚). High winding number of topological phase in non-unitary periodic quantum walk[J]. 中国物理B, 2021, 30(10): 100301-100301.

Yali Jia(贾雅利) and Zhi-Jian Li(李志坚). High winding number of topological phase in non-unitary periodic quantum walk[J]. Chin. Phys. B, 2021, 30(10): 100301-100301.

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High winding number of topological phase in non-unitary periodic quantum walk

High winding number of topological phase in non-unitary periodic quantum walk

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