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.

arXiv comment7+16 pages, 1+5 figure

References in corpus (34)

• Weyl and Dirac Semimetals in Three Dimensional Solids
• Topological Field Theory of Time-Reversal Invariant Insulators
• Edge states and topological invariants of non-Hermitian systems
• The Chiral Magnetic Effect
• The effects of topological charge change in heavy ion collisions: "Event by event P and CP violation"
• Observation of the chiral anomaly induced negative magneto-resistance in 3D Weyl semi-metal TaAs
• Symmetry and Topology in Non-Hermitian Physics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Seeing the magnetic monopole through the mirror of topological surface states
• Anatomy of skin modes and topology in non-Hermitian systems
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Weyl semimetal with broken time reversal and inversion symmetries
• Chiral anomaly and transport in Weyl metals
• Topological states of non-Hermitian systems
• Notes on Anomaly Induced Transport
• Tunable Casimir repulsion with three dimensional topological insulators
• Experimental tests of the chiral anomaly magnetoresistance in the Dirac-Weyl semimetals Na${}_3$Bi and GdPtBi
• Topological Correspondence between Hermitian and Non-Hermitian Systems: Anomalous Dynamics
• On the search for the chiral anomaly in Weyl semimetals: The negative longitudinal magnetoresistance
• Exceptional Links and Twisted Fermi Ribbons in non-Hermitian Systems
• Witten effect in a crystalline topological insulator
• Pseudo-electromagnetic fields in topological semimetals
• Topological symmetry classes for non-Hermitian models and connections to the bosonic Bogoliubov-de Gennes equation
• Non-Hermitian Weyl Physics in Topological Insulator Ferromagnet Junctions
• Topological Field Theory of Non-Hermitian Systems
• Gravitational and Chiral Anomalies in the Running Vacuum Universe and Matter-Antimatter Asymmetry
• Random matrices beyond the Cartan classification
• Topology and Observables of the Non-Hermitian Chern Insulator
• Chiral Anomaly in Interacting Condensed Matter Systems
• Non-Hermitian Chiral Magnetic Effect in Equilibrium
• Chiral Anomaly, Topological Field Theory, and Novel States of Matter
• The Chiral Anomaly, Dirac and Weyl Semimetals, and Force-Free Magnetic Fields

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