Quantum anomalous Hall conductivity on the background of Lorentz violating c -tensor

We investigate the quantum anomalous Hall effect in a (2+1)-dimensional fermionic system with a violation of emergent Lorentz invariance parametrized by the constant tensor c μν . Through explicit one-loop calculations, we derive the polarization tensor and obtain the Hall conductivity using the Kubo formula. The conductivity exhibits explicit dependence on the Lorentz-violating parameters through the modified dispersion relation for the fermions. In the static limit (ω → 0), we recover the universal quantized value σ Hall = ±2αsgn(m), demonstrating the robustness of topological response against this Lorentz-violating background.