Topological Phases of Non-Hermitian Systems

By Z. Gong, Yuto Ashida, K. Kawabata, K. Takasan, S. Higashikawa, Masahito Ueda. Physical Review X, 2018

1,282 citations recorded by the source corpus.

Recent experimental advances in controlling dissipation have brought about unprecedented flexibility in engineering non-Hermitian Hamiltonians in open classical and quantum systems. 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 the K-theory to systematically classify all the non-Hermitian topological phases in the Altland-Zirnbauer 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 a Z2 topological index for arbitrary quantum channels. Our work lays the cornerstone for a unified understanding of the role of topology in non-Hermitian systems.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/2d4f6d89cf92551ea118e4542c38aeb8d4ec122b

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Citations in the corpus

Exceptional points in optics and photonics (2019, background): “Inspired by the periodic table of topological insulators, a systematic classification of topological phases of non-Hermitian systems has also been presented (118).”
Experimental realization of a Weyl exceptional ring (2018, background): “[57] Zongping Gong, Yuto Ashida, Kohei Kawabata, Kazuaki Takasan, Sho Higashikawa, and Masahito Ueda, “Topological phases of non-Hermitian systems,” arXiv:1802.”
Non-Hermitian systems and topology: A transfer-matrix perspective (2018, background): “The problem of restoring the bulk-boundary correspondence by defining a bulk invariant that can predict the existence of topologically protected boundary modes is rather subtle [51, 52].”
Perspective on topological states of non-Hermitian lattices (2019, background): “lattice may become devoid of extended states [45, 46], an effect termed non-Hermitian skin effect [47, 48]. On the other hand, there is an intense activity in the search of a consistent classiﬁcation [49, 50, 51, 52, 53], the deﬁnition of the topological invariants [54, 55, 56], and the search of a ”
A review on non-Hermitian skin effect (2022, background): “manifested in the semi-infinite truncations of the non-Hermitian systems with only one boundary [43,144].”
Roadmap on topological photonics (2022, positive): “We are beginning to learn that non-hermiticity not only quantitatively modifies, but qualitatively expands existing classifications of Hermitian topological systems [63].”