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arXiv:2608.04083

Breakdown of Monotonic Impurity Entropy Flow in $\mathscr{PT}$-Symmetric Multichannel Kondo Systems

Pradip Kattel, Abay Zhakenov, Natan Andrei

cond-mat.str-elcond-mat.stat-mechhep-thmath-phquant-phSubmitted Aug 4, 2026• Announced Aug 6, 2026• 0 citations
v1 · Aug 4, 2026v2 · Aug 13, 2026
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Abstract

We study a $\mathscr{PT}$-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 $T_K$ 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 $\mathscr{PT}$-unbroken, whereas the YSR phase spontaneously breaks $\mathscr{PT}$ symmetry. Using a generalized thermodynamic Bethe Ansatz, we determine the impurity free energy and Affleck--Ludwig $g$-function throughout the $\mathscr{PT}$-unbroken phases. In the Kondo phase, the defect RG flow connects the ultraviolet and infrared conformal fixed points, with the impurity entropy flowing from $2\ln2$ to $2\ln\left[2\cos\left(\fracπ{n+2}\right)\right]$, 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.

Comments
The arXiv abstract has been shortened to comply with the abstract length limit; the full abstract appears in the manuscript

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Breakdown of Monotonic Impurity Entropy Flow in PT\mathscr{PT}PT-Symmetric Multichannel Kondo Systems
We study a PT\mathscr{PT}PT-symmetric non-Hermitian multichannel Kondo model consisting of a pair of spin-12\frac1221​ impurities coupled to nnn conduction-electron channels through complex-conjugate Kondo couplings. The impurity renormalization-group (RG) flow is characterized by the Kondo scale TKT_KTK​ and a dimensionless non-Hermiticity parameter ααα. As ααα 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 PT\mathscr{PT}PT-unbroken, whereas the YSR phase spontaneously breaks PT\mathscr{PT}PT symmetry. Using a generalized thermodynamic Bethe Ansatz, we determine the impurity free energy and Affleck--Ludwig ggg-function throughout the PT\mathscr{PT}PT-unbroken phases. In the Kondo phase, the defect RG flow connects the ultraviolet and infrared conformal fixed points, with the impurity entropy flowing from 2ln⁡22\ln22ln2 to 2ln⁡[2cos⁡(πn+2)]2\ln\left[2\cos\left(\fracπ{n+2}\right)\right]2ln[2cos(n+2π​)], 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 ggg-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.
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A conformal-field-theory approach has recently been developed for quantum-impurity problems including the ``overscreened'' multichannel Kondo model. We present the details of our calculation of the single-fermion Green's function. The universal zero-temperature resistivity and leading temperature-dependent term are derived. Effects of particle-hole symmetry breaking are included. We also give our perturbative proof of the ``g theorem'' governing the change in residual entropy under a renormalization-group flow between two boundary fixed points.
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