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We propose a general construction of symmetry protected Lorentz invariantnon-Hermitian (NH) Dirac semimetals (DSMs), realized by invoking masslikeanti-Hermitian Dirac operators to its Hermitian counterpart. They featurepurely real or imaginary isotropic linear band dispersion, yielding a vanishingdensity of states. Dynamic mass orderings in NH DSMs thus take place for strongHubbardlike local interactions through a quantum phase transition where nodalNH Dirac quasiparticles are strongly coupled with bosonic order-parameterfluctuations, hosting a non-Fermi liquid, beyond which the system becomes aninsulator. Depending on the internal Clifford algebra between the NH Diracoperator and candidate mass order-parameter, the resulting quantum criticalfluid either remains coupled with the environment or recovers full Hermiticityby decoupling from the bath, while always enjoying an emergent Yukawa-Lorentzsymmetry in terms of a unique velocity. We showcase the competition betweensuch mass orderings, their hallmarks on quasiparticle spectra in the orderedphases, and the relevance of our findings in correlated designer NH Diracmaterials.

Yukawa-Lorentz Symmetry in Non-Hermitian Dirac Materials