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Topological Phases of Non-Hermitian Systems

Physical review. X, 2018-09, Vol.8 (3), p.031079, Article 031079 [Peer Reviewed Journal]

2018. This work is licensed under https://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. ;ISSN: 2160-3308 ;EISSN: 2160-3308 ;DOI: 10.1103/PhysRevX.8.031079

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  • Title:
    Topological Phases of Non-Hermitian Systems
  • Author: Gong, Zongping ; Ashida, Yuto ; Kawabata, Kohei ; Takasan, Kazuaki ; Higashikawa, Sho ; Ueda, Masahito
  • Subjects: Amplitudes ; Bose-Einstein condensates ; Exchanging ; Excitons ; Hamiltonian functions ; Lattice vibration ; Metallicity ; Periodic table ; Phases ; Polaritons ; Quantum mechanics ; Robustness (mathematics) ; Superconductors ; Symmetry ; Topological insulators ; Topology ; Wave packets ; Winding
  • Is Part Of: Physical review. X, 2018-09, Vol.8 (3), p.031079, Article 031079
  • Description: While Hermiticity lies at the heart of quantum mechanics, recent experimental advances in controlling dissipation have brought about unprecedented flexibility in engineering non-Hermitian Hamiltonians in open classical and quantum systems. Examples include parity-time-symmetric optical systems with gain and loss, dissipative Bose-Einstein condensates, exciton-polariton systems, and biological networks. A particular interest centers on the topological properties of non-Hermitian systems, which exhibit unique phases with no Hermitian counterparts. However, no systematic understanding in analogy with the periodic table of topological insulators and superconductors has been achieved. In this paper, we develop a coherent framework of topological phases of non-Hermitian systems. After elucidating the physical meaning and the mathematical definition of non-Hermitian topological phases, we start with one-dimensional lattices, which exhibit topological phases with no Hermitian counterparts and are found to be characterized by an integer topological winding number even with no symmetry constraint, reminiscent of the quantum-Hall insulator in Hermitian systems. A system with a nonzero winding number, which is experimentally measurable from the wave-packet dynamics, is shown to be robust against disorder, a phenomenon observed in the Hatano-Nelson model with asymmetric hopping amplitudes. We also unveil a novel bulk-edge correspondence that features an infinite number of (quasi)edge modes. We then apply theKtheory to systematically classify all the non-Hermitian topological phases in the Altland-Zirnbauer (AZ) classes in all dimensions. The obtained periodic table unifies time-reversal and particle-hole symmetries, leading to highly nontrivial predictions such as the absence of non-Hermitian topological phases in two dimensions. We provide concrete examples for all the nontrivial non-Hermitian AZ classes in zero and one dimensions. In particular, we identify aZ2topological index for arbitrary quantum channels (completely positive trace-preserving maps). Our work lays the cornerstone for a unified understanding of the role of topology in non-Hermitian systems.
  • Publisher: College Park: American Physical Society
  • Language: English
  • Identifier: ISSN: 2160-3308
    EISSN: 2160-3308
    DOI: 10.1103/PhysRevX.8.031079
  • Source: DOAJ Directory of Open Access Journals
    ROAD: Directory of Open Access Scholarly Resources
    ProQuest Central
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