Non-Hermitian chiral anomalies

Abstract

The chiral anomaly underlies a broad number of phenomena, from enhanced electronic transport in topological metals to anomalous currents in the quark-gluon plasma. The discovery of topological states of matter in non-Hermitian systems -- effective descriptions of dissipative systems -- raises the question of whether there are anomalous conservation laws that remain unaccounted for. To answer this question, we consider both $1+1$ and $3+1$ dimensions, presenting a unified formulation to calculate anomalous responses in Hermitianized, anti-Hermitianized and non-Hermitian systems of massless electrons with complex Fermi velocities coupled to non-Hermitian gauge fields. Our results indicate that the quantum conservation laws of chiral currents of non-Hermitian systems are not related to those in Hermitianized and anti-Hermitianized systems, as would be expected classically, due to novel anomalous terms that we derive. These may have implications for a broad class of emerging experimental systems that realize non-Hermitian Hamiltonians.

7+16 pages, 1+5 figure

References in corpus (9)

• Topological Field Theory of Time-Reversal Invariant Insulators
• The Chiral Magnetic Effect
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Chiral anomaly and transport in Weyl metals
• Tunable Casimir repulsion with three dimensional topological insulators
• Topological Field Theory of Non-Hermitian Systems
• Random matrices beyond the Cartan classification
• Chiral Anomaly in Interacting Condensed Matter Systems

Cited by in corpus (10)

• Topological Non-Hermitian skin effect
• Non-Hermitian Mott Skin Effect
• Symmetry-protected exceptional and nodal points in non-Hermitian systems
• Topological phase diagrams of exactly solvable non-Hermitian interacting Kitaev chains
• Scrambling and operator entanglement in local non-Hermitian quantum systems
• Infernal and Exceptional Edge Modes: Non-Hermitian Topology Beyond the Skin Effect
• Protection of all nondefective twofold degeneracies by anti-unitary symmetries in non-Hermitian systems
• Topological Electromagnetic Effects and Higher Second Chern Numbers in Four-Dimensional Gapped Phases
• Non-Hermitian chiral anomalies in interacting systems
• Anomalous Chiral Anomaly in Spin-1 Fermionic Systems