Topological Duality in Floquet and Non-Hermitian Dynamical Anomalies: Extended Nielsen-Ninomiya Theorem and Chiral Magnetic Effect

According to conventional theory, bulk anomalous gapless states are prohibited in lattices. However, Floquet and non-Hermitian systems may dynamically realize such quantum anomalies in the bulk. Here, we present an extension of the Nielsen-Ninomiya theorem that is valid even in the presence of the bulk quantum anomaly. Particularly, the extended theorem establishes the exact
correspondence between bulk topological numbers and bulk anomalous gapless modes in Floquet and non-Hermitian systems. Applying our theorem, we predict a new type of chiral magnetic effect—non-Hermitian chiral magnetic skin effect. Our work is based on the duality between Floquet and non-Hermitian systems and provides a unified understanding of the dynamical anomalies.
[1] T. Bessho and M. Sato, arXiv:2006.04204.