Phase diagram and quench dynamics of a periodically driven Haldane model

doi:10.1088/1674-1056/ad4eb3

中国物理B ›› 2024, Vol. 33 ›› Issue (9): 90309-090309.doi: 10.1088/1674-1056/ad4eb3

Phase diagram and quench dynamics of a periodically driven Haldane model

Minxuan Ren(任民烜)†, Han Yang(杨焓), and Mingyuan Sun(孙明远)

School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China

收稿日期:2024-03-14 修回日期:2024-05-14 接受日期:2024-05-22 出版日期:2024-08-15 发布日期:2024-08-15
通讯作者: Minxuan Ren E-mail:renminxuanphy@bupt.edu.cn
基金资助:
We thank Ping Fang, Jieyun Yan, and Yueheng Lan for inspiring discussions. The project was supported by the National Natural Science Foundation of China (Grant No. 12004049).

Phase diagram and quench dynamics of a periodically driven Haldane model

Minxuan Ren(任民烜)†, Han Yang(杨焓), and Mingyuan Sun(孙明远)

School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China

Received:2024-03-14 Revised:2024-05-14 Accepted:2024-05-22 Online:2024-08-15 Published:2024-08-15
Contact: Minxuan Ren E-mail:renminxuanphy@bupt.edu.cn
Supported by:
We thank Ping Fang, Jieyun Yan, and Yueheng Lan for inspiring discussions. The project was supported by the National Natural Science Foundation of China (Grant No. 12004049).

摘要/Abstract

摘要： We investigate a periodically driven Haldane model subjected to a two-stage driving scheme in the form of a step function. By using the Floquet theory, we obtain the topological phase diagram of the system. We also find that anomalous Floquet topological phases exist in the system. Focusing on examining the quench dynamics among topological phases, we analyze the site distribution of the $0$-mode and $\pi$-mode edge states in long-period evolution after a quench. The results demonstrate that, under certain conditions, the site distribution of the $0$-mode can be confined at the edge even in long-period evolution. Additionally, both the $0$-mode and $\pi$-mode can recover and become confined at the edge in long-period evolution when the post-quench parameters $\left( T,\frac{M_2}{M_1} \right) $ in the phase diagram cross away from the phase boundary $\frac{M_2}{M_1}=\frac{6\sqrt{3} t_2}{M_1}-1$. Furthermore, we conclude that whether the edge state is confined at the edge in the long-period evolution after a quench depends on the similarity of the edge states before and after the quench. Our findings reveal some new characteristics of quench dynamics in a periodically driven system.

关键词: Floquet system, Haldane model, quench dynamics, topological phase diagram

Abstract: We investigate a periodically driven Haldane model subjected to a two-stage driving scheme in the form of a step function. By using the Floquet theory, we obtain the topological phase diagram of the system. We also find that anomalous Floquet topological phases exist in the system. Focusing on examining the quench dynamics among topological phases, we analyze the site distribution of the $0$-mode and $\pi$-mode edge states in long-period evolution after a quench. The results demonstrate that, under certain conditions, the site distribution of the $0$-mode can be confined at the edge even in long-period evolution. Additionally, both the $0$-mode and $\pi$-mode can recover and become confined at the edge in long-period evolution when the post-quench parameters $\left( T,\frac{M_2}{M_1} \right) $ in the phase diagram cross away from the phase boundary $\frac{M_2}{M_1}=\frac{6\sqrt{3} t_2}{M_1}-1$. Furthermore, we conclude that whether the edge state is confined at the edge in the long-period evolution after a quench depends on the similarity of the edge states before and after the quench. Our findings reveal some new characteristics of quench dynamics in a periodically driven system.

Key words: Floquet system, Haldane model, quench dynamics, topological phase diagram

中图分类号: (Phases: geometric; dynamic or topological)

03.65.Vf

03.65.Ge (Solutions of wave equations: bound states)

Minxuan Ren(任民烜), Han Yang(杨焓), and Mingyuan Sun(孙明远). Phase diagram and quench dynamics of a periodically driven Haldane model[J]. 中国物理B, 2024, 33(9): 90309-090309.

Minxuan Ren(任民烜), Han Yang(杨焓), and Mingyuan Sun(孙明远). Phase diagram and quench dynamics of a periodically driven Haldane model[J]. Chin. Phys. B, 2024, 33(9): 90309-090309.

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Phase diagram and quench dynamics of a periodically driven Haldane model

Phase diagram and quench dynamics of a periodically driven Haldane model

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