Microscopic emergence of non-Hermitian Dirac terms from bath coupling

Establish a precise microscopic derivation showing how coupling a tilted Dirac material to an external excitation bath characterized by a specific spectral function generates the effective non-Hermitian terms used in the tilted non-Hermitian Dirac Hamiltonian, including the anti-Hermitian linear-in-momentum component constructed via a mass matrix M that anticommutes with the Hermitian Dirac Hamiltonian and the Hermitian tilt term proportional to T k_x. Determine how the bath’s spectral properties map quantitatively onto the effective parameters (such as the non-Hermitian velocity parameter β and the tilt parameter α) and matrix structures (M and T) in the low-energy theory.

Background

The paper studies tilted non-Hermitian Dirac fermions near quantum criticality and shows that Yukawa-Lorentz symmetry emerges, with the tilt and velocity anisotropy becoming irrelevant at the quantum critical point. The non-Hermitian piece of the Dirac Hamiltonian is linked to nonreciprocal hoppings on the honeycomb lattice, and the tilt can be introduced via uniaxial strain.

While the effective field-theoretic description for the non-Hermitian terms is established and their critical behavior analyzed, a detailed microscopic mechanism that derives these effective terms directly from coupling to a specific excitation bath (fermionic or bosonic) with a given spectral function remains to be formulated. Clarifying this mapping would enable controlled engineering of non-Hermitian terms in Dirac materials.