Quantum Electrodynamics of Non-Hermitian Dirac Fermions

Abstract

We develop an effective quantum electrodynamics for non-Hermitian (NH) Dirac materials interacting with photons. These systems are described by nonspatial symmetry protected Lorentz invariant NH Dirac operators, featuring two velocity parameters $v_{{}_{\mathrm{H}}}$ and $v_{{}_{\mathrm{NH}}}$ associated with the standard Hermitian and a masslike anti-Hermitian Dirac operators, respectively. They display linear energy-momentum relation, however, in terms of an effective Fermi velocity $v_{{}_{\mathrm{F}}}=\sqrt{v_{{}_{\mathrm{H}}}^2-v_{{}_{\mathrm{NH}}}^2}$ of NH Dirac fermions. Interaction with the fluctuating electromagnetic radiation then gives birth to an emergent Lorentz symmetry in this family of NH Dirac materials in the deep infrared regime, where the system possesses a unique terminal velocity $v_{{}_{\mathrm{F}}}=c$, with $c$ being the speed of light. While in two dimensions such a terminal velocity is set by the speed of light in the free space, dynamic screening in three spatial dimensions permits its nonuniversal values. Manifestations of such an emergent spacetime symmetry on the scale dependence of various physical observables in correlated NH Dirac materials are discussed.

arXiv comment19 Pages, 3 Figures: Published version in Journal of High Energy Physics

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• Model non-Hermitian topological operators without skin effect: A general principle of construction
• Yukawa-Lorentz Symmetry of Tilted Non-Hermitian Dirac Semimetals at Quantum Criticality
• Non-Hermitian catalysis of spontaneous symmetry breaking on Euclidean and hyperbolic lattices
• Axionic quantum criticality of generalized Weyl semimetals
• Zero modes and index theorems for non-Hermitian Dirac fermions
• Minimal Hamiltonian deformations as bulk probes of effective non-Hermiticity in Dirac materials
• Exceptional flat bands in bipartite non-Hermitian lattices
• Physical constraints on effective non-Hermitian systems