Revealing the Phase Diagram of Kitaev Materials by Machine Learning: Cooperation and Competition between Spin Liquids
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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-Γ 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 × 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 × Z_3 orders exhibit spin structure factors that are similar to the ones seen in neutron scattering data of the spin-liquid candidate α-RuCl_3. These orders feature a novel spin-lattice entangled modulation and are understood as the result of the competition between Kitaev and Γ 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.
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