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arXiv · 2606.28495

Monotonic and non-Nonmonotonic Impurity Entropy flows in a $\mathscr{PT}$-Symmetric Kondo Model

Pradip Kattel·Abay Zhakenov·Natan Andrei
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Abstract

Quantum impurity models provide a paradigmatic setting for studying Kondo screening, boundary criticality, and impurity entropy. While these phenomena are well understood in unitary systems, their fate in non-Hermitian many-body settings remains largely unexplored. We study a $\mathscr{PT}$-symmetric quantum impurity model consisting of a unitary SU(2)$_1$ Wess--Zumino--Witten bulk attached to two impurity spins through complex-conjugate Kondo couplings. Using an integrable lattice realization solved by the Bethe Ansatz and benchmarked against finite-temperature matrix-product-state calculations, we determine the impurity free energy, entropy, and the corresponding $g$-function. We identify three distinct impurity phases. In the Kondo-screened phase, the spectrum remains real and the impurity entropy decreases monotonically from $\ln 4$ in the ultraviolet to $0$. Remarkably, this monotonic flow persists despite the nonunitary boundary interaction, beyond the standard domain of the $g$-theorem. The Yu--Shiba--Rusinov phase instead exhibits spontaneous $\mathscr{PT}$-symmetry breaking and loss of boundary conformal invariance, while the local-moment phase displays cyclic renormalization-group flow, with identical impurity entropy and $g$-value in the ultraviolet and infrared limits.

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Pradip Kattel, Abay Zhakenov, Natan Andrei. 2026-08-13. Monotonic and non-Nonmonotonic Impurity Entropy flows in a $\mathscr{PT}$-Symmetric Kondo Model. https://arxiv.org/abs/2606.28495

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