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arXiv:cond-mat/9402083 · Nuclear Physics B

On the parafermionic scattering of an integrable Heisenberg model with impurity

Marcio Jose Martins

Published Sep 1, 1994• 6 citations
arXivHTMLPDF
DOI
10.1016/0550-3213(94)90025-6

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We construct an integrable SU(2)-invariant model consisting of the Heisenberg chain of spin 1 interacting with an impurity of spin S. This generalizes previous results by Andrei and Johannesson for the spin-(1/2 chain. The model Hamiltonian is diagonalized and the thermodynamics is obtained. For ferromagnetic coupling at low temperatures the impurity susceptibility diverges as ${T}^{\mathrm{\ensuremath{-}}2}$ and the impurity specific heat is proportional to T1/2{T}^{1/2}T1/2 for all values of the impurity spin S. For antiferromagnetic coupling and T=0 the impurity susceptibility diverges proportionally to \ensuremath{\Vert}lnH\ensuremath{\Vert} as H\ensuremath{\rightarrow}0 if S=(1/2, while if S>1 the impurity spin is only partially compensated for by the S=1 chain.
Quantum impurity models with frustrated Kondo interactions can support quantum critical points with fractionalized excitations. Recent experiments [W. Pouse et al., Nat. Phys. (2023)NPAHAX1745-247310.1038/s41567-022-01905-4] on a circuit containing two coupled metal-semiconductor islands exhibit transport signatures of such a critical point. Here, we show using bosonization that the double charge-Kondo model describing the device can be mapped in the Toulouse limit to a sine-Gordon model. Its Bethe-ansatz solution shows that a Z_{3} parafermion emerges at the critical point, characterized by a fractional 1/2ln(3) residual entropy, and scattering fractional charges e/3. We also present full numerical renormalization group calculations for the model and show that the predicted behavior of conductance is consistent with experimental results.