2026/08/04 by Pradip Kattel, Abay Zhakenov, Natan Andrei
Physics and Astronomy · Mathematics · #cond-mat.str-el #cond-mat.stat-mech #hep-th #math-ph #math.MP #quant-ph
The arXiv abstract has been shortened to comply with the abstract length limit; the full abstract appears in the manuscript
arxiv created 2026/08/04 · arxiv updated 2026/08/06
We study a \mathscrPT-symmetric non-Hermitian multichannel Kondo model consisting of a pair of spin-\frac12 impurities coupled to n conduction-electron channels through complex-conjugate Kondo couplings. The impurity renormalization-group (RG) flow is characterized by the Kondo scale TK and a dimensionless non-Hermiticity parameter α. As α increases, the exact Bethe Ansatz solution exhibits four impurity phases: overscreened Kondo, zero mode, Yu--Shiba--Rusinov (YSR), and local moment. The Kondo, zero-mode, and local-moment phases are \mathscrPT-unbroken, whereas the YSR phase spontaneously breaks \mathscrPT symmetry. Using a generalized thermodynamic Bethe Ansatz, we determine the impurity free energy and Affleck--Ludwig g-function throughout the \mathscrPT-unbroken phases. In the Kondo phase, the defect RG flow connects the ultraviolet and infrared conformal fixed points, with the impurity entropy flowing from 2ln2 to 2ln[2cos(\fracπn+2)], in agreement with defect conformal field theory. In the zero-mode phase, zero-energy impurity strings reorganize the spectrum into multiple excitation towers, while in the local-moment phase, the RG flow becomes cyclic, returning to the unscreened local-moment fixed point. We conjecture that RG irreversibility, and hence a generalized Affleck--Ludwig g-theorem, survives throughout the Kondo phase. Our exact solution nevertheless shows that a real spectrum and defect entropies consistent with defect CFT do not guarantee RG irreversibility: the impurity entropy is non-monotonic in both the zero-mode and local-moment phases.