Light-Driven Bound State of Interacting Impurities in a Dirac-Like Bath

Strongly correlated quantum impurities under periodic driving can exhibit emergent non-Hermitian phenomena, yet a microscopic understanding has been lacking. We introduce an auxiliary-fermion framework that captures the bath's spin-orbit and angular-momentum structure and generates an effective low-energy theory with symmetry-protected spin-selective gain-loss channels. Exceptional points (EPs) arise dynamically from hybridization, without inserting non-Hermitian terms by hand, while causality is preserved via sign-reversing contributions. Near EPs, eigenvector non-orthogonality strongly enhances the impurity density of states, boosting the Kondo scale according to the condition number of the effective Hamiltonian. This DOS enhancement provides a directly measurable signature of EPs in impurity systems when spin-flip processes are induced experimentally. The pseudo-Hermitian structure further enables a biorthogonal thermodynamic Bethe ansatz treatment of interactions. Our results establish a unified route by which driven environments can engineer correlated, emergent non-Hermitian impurity states, opening a new avenue to control quantum many-body systems far from equilibrium.