Quantum geometric tensor and the topological characterization of the extended Su-Schrieffer-Heeger model

doi:10.1088/1674-1056/ad1170

中国物理B ›› 2024, Vol. 33 ›› Issue (3): 30310-030310.doi: 10.1088/1674-1056/ad1170

Quantum geometric tensor and the topological characterization of the extended Su-Schrieffer-Heeger model

Xiang-Long Zeng(曾相龙), Wen-Xi Lai(赖文喜), Yi-Wen Wei(魏祎雯), and Yu-Quan Ma(马余全)^†

School of Science, Beijing Information Science and Technology University, Beijing 100192, China

收稿日期:2023-07-16 修回日期:2023-10-20 接受日期:2023-12-01 出版日期:2024-02-22 发布日期:2024-02-29
通讯作者: Yu-Quan Ma E-mail:abelish@163.com
基金资助:
Project supported by the Beijing Natural Science Foundation (Grant No. 1232026), the Qinxin Talents Program of BISTU (Grant No. QXTCP C201711), the R&D Program of Beijing Municipal Education Commission (Grant No. KM202011232017), the National Natural Science Foundation of China (Grant No. 12304190), and the Research fund of BISTU (Grant No. 2022XJJ32).

Quantum geometric tensor and the topological characterization of the extended Su-Schrieffer-Heeger model

Xiang-Long Zeng(曾相龙), Wen-Xi Lai(赖文喜), Yi-Wen Wei(魏祎雯), and Yu-Quan Ma(马余全)^†

School of Science, Beijing Information Science and Technology University, Beijing 100192, China

Received:2023-07-16 Revised:2023-10-20 Accepted:2023-12-01 Online:2024-02-22 Published:2024-02-29
Contact: Yu-Quan Ma E-mail:abelish@163.com
Supported by:
Project supported by the Beijing Natural Science Foundation (Grant No. 1232026), the Qinxin Talents Program of BISTU (Grant No. QXTCP C201711), the R&D Program of Beijing Municipal Education Commission (Grant No. KM202011232017), the National Natural Science Foundation of China (Grant No. 12304190), and the Research fund of BISTU (Grant No. 2022XJJ32).

摘要/Abstract

摘要： We investigate the quantum metric and topological Euler number in a cyclically modulated Su-Schrieffer-Heeger (SSH) model with long-range hopping terms. By computing the quantum geometry tensor, we derive exact expressions for the quantum metric and Berry curvature of the energy band electrons, and we obtain the phase diagram of the model marked by the first Chern number. Furthermore, we also obtain the topological Euler number of the energy band based on the Gauss-Bonnet theorem on the topological characterization of the closed Bloch states manifold in the first Brillouin zone. However, some regions where the Berry curvature is identically zero in the first Brillouin zone result in the degeneracy of the quantum metric, which leads to ill-defined non-integer topological Euler numbers. Nevertheless, the non-integer "Euler number" provides valuable insights and an upper bound for the absolute values of the Chern numbers.

关键词: quantum geometric tensor, topological Euler number, Chern number, Berry curvature, quantum metric, Su-Schrieffer-Heeger (SSH) model

Abstract: We investigate the quantum metric and topological Euler number in a cyclically modulated Su-Schrieffer-Heeger (SSH) model with long-range hopping terms. By computing the quantum geometry tensor, we derive exact expressions for the quantum metric and Berry curvature of the energy band electrons, and we obtain the phase diagram of the model marked by the first Chern number. Furthermore, we also obtain the topological Euler number of the energy band based on the Gauss-Bonnet theorem on the topological characterization of the closed Bloch states manifold in the first Brillouin zone. However, some regions where the Berry curvature is identically zero in the first Brillouin zone result in the degeneracy of the quantum metric, which leads to ill-defined non-integer topological Euler numbers. Nevertheless, the non-integer "Euler number" provides valuable insights and an upper bound for the absolute values of the Chern numbers.

Key words: quantum geometric tensor, topological Euler number, Chern number, Berry curvature, quantum metric, Su-Schrieffer-Heeger (SSH) model

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

03.65.Vf

73.43.Nq (Quantum phase transitions) 75.10.Pq (Spin chain models) 05.70.Jk (Critical point phenomena)

Xiang-Long Zeng(曾相龙), Wen-Xi Lai(赖文喜), Yi-Wen Wei(魏祎雯), and Yu-Quan Ma(马余全). Quantum geometric tensor and the topological characterization of the extended Su-Schrieffer-Heeger model[J]. 中国物理B, 2024, 33(3): 30310-030310.

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Quantum geometric tensor and the topological characterization of the extended Su-Schrieffer-Heeger model

Quantum geometric tensor and the topological characterization of the extended Su-Schrieffer-Heeger model

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