Nielsen-Ninomiya Theorem with Bulk Topology: Duality in Floquet and Non-Hermitian Systems

TL;DR

This paper extends the Nielsen-Ninomiya theorem to dynamical systems, revealing how bulk topology allows chiral fermions in driven and non-Hermitian systems, and predicts a new chiral magnetic effect.

Contribution

It introduces a generalized Nielsen-Ninomiya theorem for dynamical systems, unifies treatment of Floquet and non-Hermitian systems, and predicts a novel non-Hermitian chiral magnetic skin effect.

Findings

Extended theorem permits bulk chiral fermions due to topology.

Unified duality framework for Floquet and non-Hermitian systems.

Prediction of non-Hermitian chiral magnetic skin effect.

Abstract

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 non-chiral 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.