Revealing the Phase Diagram of Kitaev Materials by Machine Learning: Cooperation and Competition between Spin Liquids

Ke Liu, Nicolas Sadoune, Nihal Rao, Jonas Greitemann, Lode Pollet

Kitaev materials are promising materials for hosting quantum spin liquids and investigating the interplay of topological and symmetry-broken phases. We use an unsupervised and interpretable machine-learning method, the tensorial-kernel support vector machine, to study the classical honeycomb Kitaev-$\Gamma$ model in a magnetic field. Our machine learns the global phase diagram and the associated analytical order parameters, including several distinct spin liquids, two exotic $S_3$ magnets, and two modulated $S_3 \times Z_3$ magnets. We find that the extension of Kitaev spin liquids and a field-induced suppression of magnetic orders already occur in the large-$S$ limit, implying that critical parts of the physics of Kitaev materials can be understood at the classical level. Moreover, the two $S_3 \times Z_3$ orders exhibit spin structure factors that are similar to the ones seen in neutron scattering data of the spin-liquid candidate $\alpha$-$\mathrm{RuCl}_3$. These orders feature a novel spin-lattice entangled modulation and are understood as the result of the competition between Kitaev and $\Gamma$ spin liquids. Our work provides the first instance where a machine detects new phases and paves the way towards developing automated tools to explore unsolved problems in many-body physics.

Knowledge Graph

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