2026/04/30 by Vinayak M. Kulkarni
Physics and Astronomy · Mathematics · #math-ph #math.MP #msc:81R12 #msc:82B23 #msc:81Q12 #msc:15A20
25 pages, 2 figures; 10-page Supplemental Material. Completely revised title and construction: exact finite-U Anderson R-matrix, bounded finite-ring twist, YBE/RLL/RTT, symmetry-protected many-body Jordan theorem, projective Laguerre root contraction, and graded 16x16 Hubbard twist compatibility. Reproducibility archive: https://doi.org/10.5281/zenodo.21794458
arxiv created 2026/08/05 · arxiv updated 2026/08/06
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=γσx+iβσz, 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-2εd-U)/(2UΓA) and yields YBE, RLL, and twisted RTT relations for arbitrary particle number. At β2=γ2, 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=∞ with scaled positions fixed by Lr(-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.