Machine-Learned Phase Diagrams of Generalized Kitaev Honeycomb Magnets

Abstract

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-$\Gamma$ ($J$-$K$-$\Gamma$) 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 $S_3\times Z_3$ phase, which emerges through the competition between the Kitaev and $\Gamma$ spin liquids, against Heisenberg interactions. The results imply that, in the restricted parameter space spanned by the three primary exchange interactions -- $J$, $K$, and $\Gamma$, the representative Kitaev material $\alpha$-${\mathrm{RuCl}}_3$ lies close to the boundaries of several phases, including a simple ferromagnet, the unconventional $S_3\times Z_3$ and nested zigzag-stripy magnets. A zigzag order is stabilized by a finite ${\Gamma }^{\prime }$ and/or $J_3$ term, whereas the four magnetic orders may compete in particular if ${\Gamma }^{\prime }$ is anti-ferromagnetic.

arXiv comment13 pages, 12 figures, 1 table; expanded discussions, added references; as published

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