  A non-linear dispersion can significantly impact the Kondo problem, resulting
in anomalous effects on electronic transport. By analyzing a special bath with
a $\theta=\frac{\pi}{3}$ symmetry rotation in the Brillouin zone or 3-fold
symmetry in momentum, we derive an effective spin-spin interacting model.
Combining the anisotropic Dzyaloshinskii-Moriya (DM) interaction with
non-linear dispersion can lead to exceptional points $(E_p)$ in a Hermitian
model. Our RG analysis reveals that the spin relaxation time has the signature
of coalescence in momentum-resolved couplings and an ideal logarithmic
divergence in resistivity over a range of nonlinearity ($\beta$). The effective
model at the impurity subspace has a Lie group structure of Dirac matrices. We
show nontrivial renormalization within a Poorman approximation with the
inclusion of potential scattering, and the invariant obtained will not be
altered by potential scattering. We expand the model to a two-impurity Kondo
model and investigate the Kondo destruction and anomalous spin transport
signature by calculating the spin-relaxation time ($\tau$).Analysis of RG
equations zeros and poles show a "Sign Reversion" regime exists for a Hermitian
problem with a critical value of nonlinear coupling $J_{k^3}$. Our results show
the existence of an out-of-phase RKKY oscillation above and below the critical
value of the chemical potential.
