Takumi Bessho

Yukawa Institute for Theoretical Physics
Kyoto University
Japan

Topological duality in Floquet and non-Hermitian systems

In Floquet systems or periodically driven systems, anomaly does not need to be cancelled [1,2]. For example, Floquet effective Hamiltonian of thouless pumping can have only one right-going mode in one dimension [1]. Single Weyl dispersion can be constructed in three dimensions [2]. On the other hand, in non-Hermitian systems, anomaly cancellation also needs not to occur [3]. We unify these anomalies and construct an extended Nielsen-Ninomiya theorem for Floquet systems by using this duality.

[1] L. Privitera, A. Russomanno, R. Citro, G.E. Santoro, Phys. Rev. Lett. 120, 106601 (2018).
[2] S. Higashikawa, M. Nakagawa, and M. Ueda, Phys. Rev. Lett. 123, 066403 (2019).
[3] J. Y. Lee, J. Ahn, H. Zhou, A. Vishwanath, arXiv:1906.08782.