Machine-Learned Phase Diagrams of Generalized Kitaev Honeycomb Magnets
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We use a recently developed interpretable and unsupervised machine-learning method, the tensorial kernel support vector machine (TK-SVM), to investigate the low-temperature classical phase diagram of a generalized Heisenberg-Kitaev-Γ (J-K-Γ) model on a honeycomb lattice. Aside from reproducing phases reported by previous quantum and classical studies, our machine finds a hitherto missed nested zigzag-stripy order and establishes the robustness of a recently identified modulated S_3 × Z_3 phase, which emerges through the competition between the Kitaev and Γ spin liquids, against Heisenberg interactions. The results imply that, in the restricted parameter space spanned by the three primary exchange interactions – J, K, and Γ, the representative Kitaev material α-RuCl_3 lies close to the interface of several phases, including a simple ferromagnet, and the unconventional S_3 × Z_3 and nested zigzag-stripy magnets. A zigzag order is stabilized by a finite Γ^' and/or J_3 term, whereas the four magnetic orders may compete in particular if Γ^' is anti-ferromagnetic.
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