The Nielsen-Ninomiya theorem is a fundamental theorem on the realization of chiral fermions in static lattice systems in high-energy and condensed matter physics. Here we extend the theorem in dynamical systems, which include the original Nielsen-Ninomiya theorem in the static limit. In contrast to the original theorem, which is a no-go theorem for bulk chiral fermions, the new theorem permits them due to bulk topology intrinsic to dynamical systems. The theorem is based on duality enabling a unified treatment of periodically driven systems and non-Hermitian ones. We also present the extended theorem for nonchiral gapless fermions protected by symmetry. Finally, as an application of our theorem and duality, we predict a new type of chiral magnetic effect—the non-Hermitian chiral magnetic skin effect.

• Received 8 June 2020
• Revised 13 July 2021
• Accepted 28 September 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.196404