Symmetry and Topology in Non-Hermitian Physics

Kohei Kawabata (U. Tokyo)

The past decades have witnessed a number of rich properties of non-Hermitian systems that have no counterparts in conventional Hermitian systems. Here we develop a general theory of symmetry and topology in non-Hermitian physics [1-5]. We demonstrate that non-Hermiticity unifies [1,2] and ramifies [3] the celebrated Altland-Zirnbauer symmetry for insulators and superconductors, leading to 38-fold symmetry [3] instead of the 10-fold one. This 38-fold symmetry describes intrinsic non-Hermitian topological phases [3,4] as well as non-Hermitian random matrices [5]. Moreover, we reveal that two types of energy gaps are relevant for non-Hermitian systems due to the complex-valued nature of energy spectra [3], both of which constitute non-Hermitian topology. On the basis of these fundamental insights in non-Hermitian physics, we completely classify topological phases of non-Hermitian insulators and superconductors [3], as well as semimetals that support exceptional points [4]. Our work paves the way toward unique phenomena and functionalities arising from the interplay of non-Hermiticity and topology, such as symmetry-protected topological lasers and dissipative topological quantum computation.

References:
[1] Z. Gong, Y. Ashida, K. Kawabata, K. Takasan, S. Higashikawa, and M. Ueda, Phys. Rev. X 8, 031079 (2018).
[2] K. Kawabata, S. Higashikawa, Z. Gong, Y. Ashida, and M. Ueda, Nat. Commun. 10, 297 (2019).
[3] K. Kawabata, K. Shiozaki, M. Ueda, and M. Sato, arXiv: 1812.09133.
[4] K. Kawabata*, T. Bessho*, and M. Sato, arXiv: 1902.08479 [*equal contributions; to appear in Phys. Rev. Lett.].
[5] R. Hamazaki, K. Kawabata, N. Kura, and M. Ueda, arXiv: 1904.13082.