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

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.

6+19 pages, 2+8 figures, 0+1 tables

References in corpus (19)

• The Chiral Magnetic Effect
• Topological Origin of Non-Hermitian Skin Effects
• Topological characterization of periodically-driven quantum systems
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• Nonunitary Scaling Theory of Non-Hermitian Localization
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• Floquet Semimetal with Floquet-band Holonomy
• Helical Floquet Channels in 1D Lattices
• Dissipative analog of four-dimensional quantum Hall physics

Cited by in corpus (12)

• Non-Hermitian topological phenomena: A review
• Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect
• Higher rank chirality and non-Hermitian skin effect in a topolectrical circuit
• Dynamical Degeneracy Splitting and Directional Invisibility in Non-Hermitian Systems
• Bulk-boundary correspondence in point-gap topological phases
• Mixed higher-order topology: boundary non-Hermitian skin effect induced by a Floquet bulk
• Chiral metals and entrapped insulators in a one-dimensional topological non-Hermitian system
• Dynamical signatures of point-gap Weyl semimetal
• Generalized Fermion Doubling Theorems: Classification of 2D Nodal Systems in Terms of Wallpaper Groups
• Exceptional mode topological surface laser
• Anomaly-induced edge currents in hydrodynamics with parity anomaly
• Interplay of Disorder and Point-Gap Topology: Chiral Modes, Localization and Non-Hermitian Anderson Skin Effect in One Dimension