Jordan-Twist Bethe Ansatz and Many-Body Exceptional-Point Amplification in the Finite-$U$ Anderson Impurity

Abstract

We construct an interacting integrable realization of many-body exceptional-point amplification in the static equal-velocity linearized finite-$U$ Anderson impurity. Two spin-orbit branches are linearized about counterpropagating Fermi points and folded into equal-velocity chiral components. The impurity carries the constant pseudo-Hermitian matrix $M=γσ_x+iβσ_z$, while the hybridization is a component scalar. A canonical $GL(2,\mathbb C)$ transformation preserves the Anderson interaction, and a position-dependent version maps the model to the conventional Anderson Hamiltonian plus a conserved complexified pseudospin charge with boundary twist $G=\exp(iML/v)$. The exact two-electron Anderson $R$-matrix is rational in the dressed rapidity $u(p)=p(p-2ε_d-U)/(2UΓ_A)$ and yields YBE, RLL, and twisted RTT relations for arbitrary particle number. At $β^2=γ^2$, $G$ is nontrivial unipotent. On every pseudospin-$S$ multiplet, the deformed Hamiltonian is similar to a single Jordan block of order $2S+1$; finite $U$ shifts its energy but does not split it. Approaching the unipotent point through a singularly conjugated diagonal twist, the descendant spin roots contract to $λ=\infty$ with scaled positions fixed by $L_r^{(-2S-1)}(2x)$. For the maximal descendant at large $S$, their normalized zeros converge to the Szego curve. Curvature, unequal velocities, and nonscalar channel couplings lie outside the theorem.