Yukawa-Lorentz symmetry of tilted non-Hermitian Dirac semimetals at quantum criticality

Dirac materials, hosting linearly dispersing quasiparticles at low energies, exhibit an emergent Lorentz symmetry close to a quantum critical point (QCP) separating a semimetallic state from a strongly coupled gapped insulator or superconductor. This feature appears quite robust even in open Dirac systems coupled to an environment, featuring non-Hermitian (NH) Dirac fermions: close to a strongly coupled QCP, a Yukawa-Lorentz symmetry emerges with a unique terminal velocity for both the fermion and the bosonic order-parameter fluctuations. The system can either retain non-Hermiticity or completely decouple from the environment, recovering Hermiticity as an emergent phenomenon. We show that such Yukawa-Lorentz symmetry emerges at quantum criticality even when the NH Dirac Hamiltonian includes a tilt term at the lattice scale. As demonstrated by a leading-order $\ensuremath{\epsilon}=3\ensuremath{-}d$ expansion near the $d=3$ upper critical dimension, a tilt term becomes irrelevant near the QCP separating the NH Dirac semimetal and a gapped (insulating or superconducting) phase. This behavior extends to linear-in-momentum nontilt perturbations, introducing velocity anisotropy for the Dirac quasiparticles, which also becomes irrelevant at the QCP. These predictions can be numerically tested in quantum Monte Carlo lattice simulations of NH Hubbard-like models hosting low-energy NH tilted Dirac fermions.