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arXiv:2508.10267 · Physical review. B./Physical review. B

Spin and thermal current scaling at a Y junction of XX spin chains

Domenico Giuliano, Francesco Buccheri

Published Nov 18, 2025• 0 citations
arXivHTMLPDF

Abstract

We study the boundary phase diagram and the low-temperature heat and magnetization transport at a $Y$ junction of XX spin chains. Depending on the magnetization axis anisotropy between the magnetic exchange interactions at the junction, the system exhibits two different strong-coupling regimes at low energies/temperatures, hosting a remarkable realization of, respectively, the overscreened (topological) four- and to the two-channel Kondo fixed points, both robust against anisotropies in the chain parameters and/or in the boundary couplings. Using renormalization group arguments combined with boundary conformal field theory methods, we show the instability of the former under any XY-type anisotropy at the junction. Our system allows for using the low-temperature spin and the heat conductances to evidence the fractionalization of the elementary excitations at the four-channel Kondo fixed point by means of the magnetic Wiedemann-Franz law. We caution that the instability under XY anisotropy may hinder the detection of the phenomenology related to the four-channel Kondo effect, therefore requiring careful control in experimental realizations.

DOI
10.1103/9pvr-329m

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We study the boundary phase diagram and the low-temperature heat and magnetization transport at a YYY junction of XX spin chains. Depending on the magnetization axis anisotropy between the magnetic exchange interactions at the junction, the system exhibits two different strong-coupling regimes at low energies/temperatures, hosting a remarkable realization of, respectively, the overscreened (topological) four- and to the two-channel Kondo fixed points, both robust against anisotropies in the chain parameters and/or in the boundary couplings. Using renormalization group arguments combined with boundary conformal field theory methods, we show the instability of the former under any XY-type anisotropy at the junction. Our system allows for using the low-temperature spin and the heat conductances to evidence the fractionalization of the elementary excitations at the four-channel Kondo fixed point by means of the magnetic Wiedemann-Franz law. We caution that the instability under XY anisotropy may hinder the detection of the phenomenology related to the four-channel Kondo effect, therefore requiring careful control in experimental realizations.
We study a Y junction of spin-1/2 Heisenberg chains with an interaction that breaks both time-reversal and chain exchange symmetries, but not their product nor SU(2) symmetry. The boundary phase diagram features a stable disconnected fixed point at weak coupling and a stable three-channel Kondo fixed point at strong coupling, separated by an unstable chiral fixed point at intermediate coupling. Using non-abelian bosonization and boundary conformal field theory, together with density matrix renormalization group and quantum Monte Carlo simulations, we characterize the signatures of these low-energy fixed points. In particular, we address the boundary entropy, the spin conductance, and the temperature dependence of the scalar spin chirality and the magnetic susceptibility at the boundary.
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Boundary phases and thermodynamics of the Kondo spin-sss chain: from overscreened Kondo to boundary-bound states
We study a spin-12\frac1221​ impurity coupled to the boundary of a strongly correlated spin-sss Takhtajan--Babujian chain, an integrable model whose low-energy physics is described by a perturbed SU(2)2sSU(2)_{2s}SU(2)2s​ Wess--Zumino--Witten conformal field theory. While boundary conformal field theory determines the low-energy universality class of the weak-coupling regime, exact Bethe Ansatz methods reveal a sequence of boundary quantum phase transitions in which impurity-bound states emerge and reorganize the Hilbert space into multiple excitation towers built on distinct boundary configurations. This tower restructuring provides the organizing principle for a rich boundary phase diagram extending beyond the conventional Kondo regime. Weak antiferromagnetic coupling realizes the overscreened 2s2s2s-channel Kondo universality class, whereas stronger couplings generate localized boundary modes and qualitatively new screening mechanisms. To describe the resulting thermodynamics, we develop a generalized thermodynamic Bethe Ansatz framework that captures the multi-tower structure across all regimes. The impurity entropy reproduces the boundary conformal field theory prediction in the overscreened Kondo regime but develops pronounced nonmonotonic temperature dependence once boundary-bound states appear, in quantitative agreement with large-scale finite-temperature matrix-product-operator simulations. Complementary dynamical calculations reveal sharp threshold features in the impurity spectral function that directly track the underlying tower structure. Together, boundary conformal field theory, exact Bethe Ansatz, generalized thermodynamic Bethe Ansatz, and tensor-network simulations provide a unified description of impurity screening, boundary-bound-state formation, and excitation-tower reconstruction in a correlated spin-sss chain.
The Kondo effect in a one-dimensional spin-12\frac{1}{2}21​ XXZ\mathrm{XXZ}XXZ model in the gapless XY\mathrm{XY}XY regime $(\ensuremath{-}1<\ensuremath{\Delta}<~1)$ is studied both analytically and numerically. In our model an impurity spin (S=1/2)(S=1/2)(S=1/2) is coupled to a single spin in the XXZ\mathrm{XXZ}XXZ spin chain. Perturbative renormalization-group (RG) analysis is performed for various limiting cases to deduce low-energy fixed points. It is shown that in the ground state the impurity spin is screened by forming a singlet with a spin in the host XXZ\mathrm{XXZ}XXZ chain. In the antiferromagnetic side $(0<\ensuremath{\Delta}<~1)$ the host chain is cut into two semi-infinite chains by the singlet. In the ferromagnetic side $(\ensuremath{-}1<\ensuremath{\Delta}<0),$ on the other hand, the host XXZ\mathrm{XXZ}XXZ chain remains as a single chain through ``healing'' of a weakened bond in the low-energy (long-distance) limit. The density-matrix renormalization-group method is used to study the size scaling of finite-size energy gaps and the power-law decay of correlation functions in the ground state. The numerical results are in good agreement with the predictions of the RG analysis. Low-temperature behaviors of specific heat and susceptibility are also discussed.
We study the low-temperature behavior of a boundary magnetic impurity ${S}^{\ensuremath{'}}=1/2$ in an open ferromagnetic Takhatajian-Babujian spin-SSS chain. For antiferromagnetic Kondo coupling, it is shown via the Bethe ansatz solution that the impurity spin is always locked into the critical behavior of the bulk. At low temperatures, a local composite of spin-$(S\ensuremath{-}1/2)$ forms near the impurity site and its contribution to specific heat is of simple power law T1/2.{T}^{1/2}.T1/2. The absence of the overscreened Kondo effect is due to the large correlation length of host spins which is divergent near the quantum critical point.
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