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

Abstract

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.

Figures (7)

• Figure 1: Coalescing spin and charge rapidities from the biorthogonal Bethe Ansatz. R and L denote right and left spaces; top panels show the real and imaginary parts of the rapidities. Effective flip-contribution strength $\gamma_{\mathrm{eff}}^{2}(U,\lambda)$ as a function of interaction $U$ and spin-orbit coupling $\lambda$. The colormap represents the renormalized gain--loss parameter, showing how interactions and SOC suppress the bare value $\gamma^{2}$. The black dashed contour indicates a reference level (e.g., renormalized EP boundary $\gamma_{\mathrm{eff}}^{2}=0$ or shifted threshold $\gamma_{\mathrm{eff}}^{2}=0.25$). Regions above the contour support a $\mathcal{PT}$ transition; regions below correspond to parameter regimes where interactions and hybridization lift the exceptional point.
• Figure 2: Top: Steady-state non-Hermitian impurity spectrum of the self-consistent $4\times4$ auxiliary-fermion Hamiltonian with pseudochiral hybridization $\widetilde{\beta}=\beta b_c$. Real and imaginary parts of impurity-like eigenvalues versus $\beta$ are shown. Shaded envelopes indicate $k$-resolved spread; the red marker denotes the onset of an exceptional point (EP). The divergence of the impurity-subspace condition number $\kappa_{\mathrm{imp}}=\|V_{\mathrm{imp}}\|\|V_{\mathrm{imp}}^{-1}\|$ quantifies $\mathcal{PT}$-symmetric non-orthogonality. Bottom: Real-time Heisenberg evolution of $O=|d_{\uparrow}\rangle\langle d_{\uparrow}|$ for representative $\beta$. Real part, magnitude, and complex-plane trajectory of $\langle O(t)\rangle$ show a crossover from underdamped oscillations (unbroken phase) to critical slowing near the EP and overdamping in the broken phase. Kondo scale acquires an EP-enhanced prefactor, $T_K^{\mathrm{EP}}\propto \kappa_{\mathrm{imp}}\exp[-|\epsilon_\xi|/\mathrm{Re}\,\widetilde{\beta}]$.
• Figure 3: Top: Steady-state eigenvalue spectrum $E_i(\beta)$ of the effective impurity Hamiltonian with flip self-energy set to zero, versus renormalized hybridization $\beta$. Panels show (a) real parts, (b) imaginary parts, and (c) condition number $\mathrm{cond}(R)$. Despite the absence of flip self-energy, an exceptional point (EP) persists via branch coalescence, though $\mathrm{cond}(R)$ does not diverge. Bottom: Real-time Heisenberg evolution of $O=|d_{\uparrow}\rangle\langle d_{\uparrow}|$ in the Hermitian limit. Dynamics remain norm-preserving: circular orbits form in the complex plane, unlike the spiraling motion in the fully non-Hermitian case.
• Figure 4: Fluctuation-dissipation ratio (FDR) below the exceptional point (EP), shown for $\beta_0 = 0.39$ and $\epsilon_\xi = -2$, within the $\mathcal{PT}$-symmetric phase. The two peaks correspond to balanced gain-loss features. Because $\mathcal{PT}$ symmetry is preserved, the trace of the Green's function yields a positive density of states (DOS). For $\lambda > D$ (bandwidth), the signal becomes noisier but continues to satisfy thermal equilibrium.
• Figure 5: FDR at the exceptional point, evaluated at $\beta_0 = 0.46$ with $\epsilon_\xi = -2$. Near the $\mathcal{PT}$ transition, symmetry breaking is incipient and gain-loss imbalance becomes pronounced. Although noise is enhanced at criticality, the system still attains thermal equilibrium.