Machine-Learned Phase Diagrams of Generalized Kitaev Honeycomb Magnets

TL;DR

This paper employs an interpretable machine-learning method to map the phase diagram of a generalized Kitaev honeycomb model, discovering new magnetic phases and analyzing their stability and proximity to real materials.

Contribution

It introduces the tensorial kernel support vector machine (TK-SVM) to identify and confirm phases in the $J$-$K$-$\Gamma$ model, including a previously missed nested zigzag-stripy order.

Findings

Identifies a new nested zigzag-stripy magnetic order.

Confirms the robustness of the $S_3 imes Z_3$ phase.

Shows $ m extalpha$-RuCl$_3$ is near multiple phase boundaries.

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 $\alpha$-${\rm RuCl}_3$ 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.