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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-$Gamma$ ($J$-$K$-$Gamma$) 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.
Kitaev materials are promising materials for hosting quantum spin liquids and investigating the interplay of topological and symmetry-breaking phases. We use an unsupervised and interpretable machine-learning method, the tensorial-kernel support vect
Kitaevs honeycomb-lattice spin-$1/2$ model has become a paradigmatic example for $mathbb{Z}_2$ quantum spin liquids, both gapped and gapless. Here we study the fate of these spin-liquid phases in differently stacked bilay
At zero magnetic field, a series of five phase transitions occur in Co3V2O8. The Neel temperature, TN=11.4 K, is followed by four additional phase changes at T1=8.9 K, T2=7.0 K, T3=6.9 K, and T4=6.2 K. The different phases are distinguished by the co
It is widely accepted that topological superconductors can only have an effective interpretation in terms of curved geometry rather than gauge fields due to their charge neutrality. This approach is commonly employed in order to investigate their pro
Leveraging coherent light-matter interaction in solids is a promising new direction towards control and functionalization of quantum materials, to potentially realize regimes inaccessible in equilibrium and stabilize new or useful states of matter. W