中国物理B ›› 2026, Vol. 35 ›› Issue (4): 47103-047103.doi: 10.1088/1674-1056/ae44f4

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PT phase transition and non-Hermitian skin effect in vacancy-induced subbands of the Haldane model with gain and loss

Cui-Xian Guo(郭翠仙)1,2, Xiao-Ming Zhao(赵小明)3,4, and Su-Peng Kou(寇谡鹏)5,4,†   

  1. 1 Beijing Key Laboratory of Optical Detection Technology for Oil and Gas, China University of Petroleum-Beijing, Beijing 102249, China;
    2 Basic Research Center for Energy Interdisciplinary, College of Science, China University of Petroleum-Beijing, Beijing 102249, China;
    3 Department of Physics and Institute of Theoretical Physics, University of Science and Technology Beijing, Beijing 100083, China;
    4 Key Laboratory of Multiscale Spin Physics (Ministry of Education), Beijing Normal University, Beijing 100875, China;
    5 Center for Advanced Quantum Studies, School of Physics and Astronomy, Beijing Normal University, Beijing 100875, China
  • 收稿日期:2025-11-13 修回日期:2026-02-11 接受日期:2026-02-12 发布日期:2026-04-01
  • 通讯作者: Su-Peng Kou E-mail:spkou@bnu.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 12405030), the National Key Research and Development Program of China (Grant No. 2023YFA1406704), the Open Fund of Key Laboratory of Multiscale Spin Physics (Ministry of Education) Beijing Normal University (Grant No. SPIN2024K01), Beijing National Laboratory for Condensed Matter Physics (Grant No. 2025BNLCMPKF023), the Science Foundation of China University of Petroleum, Beijing (Grant No. 2462024SZBH003), Young Elite Scientists Sponsorship Program of the Beijing High Innovation Plan (Grant No. 20250934), Guangdong Basic and Applied Basic Research Foundation (Grant No. 2023A1515110081), and Fundamental Research Funds for the Central Universities, China (Grant Nos. FRF-TP-22-098A1 and FRF-IDRY-24-28).

PT phase transition and non-Hermitian skin effect in vacancy-induced subbands of the Haldane model with gain and loss

Cui-Xian Guo(郭翠仙)1,2, Xiao-Ming Zhao(赵小明)3,4, and Su-Peng Kou(寇谡鹏)5,4,†   

  1. 1 Beijing Key Laboratory of Optical Detection Technology for Oil and Gas, China University of Petroleum-Beijing, Beijing 102249, China;
    2 Basic Research Center for Energy Interdisciplinary, College of Science, China University of Petroleum-Beijing, Beijing 102249, China;
    3 Department of Physics and Institute of Theoretical Physics, University of Science and Technology Beijing, Beijing 100083, China;
    4 Key Laboratory of Multiscale Spin Physics (Ministry of Education), Beijing Normal University, Beijing 100875, China;
    5 Center for Advanced Quantum Studies, School of Physics and Astronomy, Beijing Normal University, Beijing 100875, China
  • Received:2025-11-13 Revised:2026-02-11 Accepted:2026-02-12 Published:2026-04-01
  • Contact: Su-Peng Kou E-mail:spkou@bnu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 12405030), the National Key Research and Development Program of China (Grant No. 2023YFA1406704), the Open Fund of Key Laboratory of Multiscale Spin Physics (Ministry of Education) Beijing Normal University (Grant No. SPIN2024K01), Beijing National Laboratory for Condensed Matter Physics (Grant No. 2025BNLCMPKF023), the Science Foundation of China University of Petroleum, Beijing (Grant No. 2462024SZBH003), Young Elite Scientists Sponsorship Program of the Beijing High Innovation Plan (Grant No. 20250934), Guangdong Basic and Applied Basic Research Foundation (Grant No. 2023A1515110081), and Fundamental Research Funds for the Central Universities, China (Grant Nos. FRF-TP-22-098A1 and FRF-IDRY-24-28).

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摘要： Defects can profoundly alter the properties of quantum materials, inducing emergent phenomena beyond the scope of their parent counterparts. Here, we construct effective models to investigate the properties of vacancy-induced subbands in the Haldane model with gain and loss, revealing that their behaviors are critically dependent on the spatial configuration of the vacancy array. Specifically, a sequence of parity-time ($\mathcal{PT}$) phase transitions occurs for the one-dimensional vacancy array across different sublattices, whereas the non-Hermitian skin effect (NHSE) — with its nontrivial spectral winding — manifests in a chain confined to a single sublattice. Notably, the NHSE arises in this subband even though the parent system lacks it. Our results demonstrate that vacancy defect engineering serves as a powerful approach to generate subsystems whose properties are decoupled from the parent Hamiltonian.

关键词: non-Hermitian physics, defect, parity-time symmetry, non-Hermitian skin effect

Abstract: Defects can profoundly alter the properties of quantum materials, inducing emergent phenomena beyond the scope of their parent counterparts. Here, we construct effective models to investigate the properties of vacancy-induced subbands in the Haldane model with gain and loss, revealing that their behaviors are critically dependent on the spatial configuration of the vacancy array. Specifically, a sequence of parity-time ($\mathcal{PT}$) phase transitions occurs for the one-dimensional vacancy array across different sublattices, whereas the non-Hermitian skin effect (NHSE) — with its nontrivial spectral winding — manifests in a chain confined to a single sublattice. Notably, the NHSE arises in this subband even though the parent system lacks it. Our results demonstrate that vacancy defect engineering serves as a powerful approach to generate subsystems whose properties are decoupled from the parent Hamiltonian.

Key words: non-Hermitian physics, defect, parity-time symmetry, non-Hermitian skin effect

中图分类号:  (Impurity and defect levels)

  • 71.55.-i
03.65.Yz (Decoherence; open systems; quantum statistical methods) 11.30.Er (Charge conjugation, parity, time reversal, and other discrete symmetries) 73.20.-r (Electron states at surfaces and interfaces)