Minimal Hamiltonian deformations as bulk probes of effective non-Hermiticity in Dirac materials

TL;DR

This paper investigates how minimal Hamiltonian deformations can serve as bulk probes to detect effective non-Hermiticity in Dirac materials, especially in regimes where the spectrum appears Hermitian-like.

Contribution

It introduces a response-based diagnostic framework using minimal pseudo-Lorentz-symmetry-breaking deformations to distinguish observable effects of non-Hermiticity.

Findings

Tilt affects the density of states with NH-dependent slope.

Velocity anisotropy can be captured by effective velocity reparametrization.

Quantum metric and optical conductivities are NH-insensitive benchmarks.

Abstract

Non-Hermitian (NH) Dirac semimetals describe open gain--loss systems. Yet at charge neutrality, models featuring real spectrum often look Hermitian-like, with NH effects absorbed into renormalized band parameters. Here, we show that a response-based diagnostic of effective non-Hermiticity can be formulated using minimal pseudo-Lorentz-symmetry-breaking deformations, which separate observables that remain captured by parameter redefinitions from those that exhibit irreducible NH structure. For a two-dimensional NH Dirac semimetal in the weak-NH, real-spectrum regime, we analyze Dirac-cone tilt and velocity anisotropy and compute representative probes of spectral structure, quantum geometry, optical response, and viscoelasticity at zero temperature. We find that tilt yields an NH-dependent slope of the density of states that cannot be collapsed to a single effective velocity, while velocity anisotropy can be captured by effective-velocity reparametrization. Furthermore, the quantum metric and collisionless optical conductivities provide NH-insensitive benchmarks (with the nonlinear conductivity symmetry selected), whereas the shear viscosity offers a discriminator through its tensor structure. Our results identify minimal deformations and bulk response channels that enable access to effective non-Hermiticity even when the spectrum remains real.