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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 vector machine, to study the honeycomb Kitaev-$Gamma$ model in a magnetic field. Our machine learns the global classical 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 order 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 are induced by competition between Kitaev and $Gamma$ spin liquids and feature a different type of spin-lattice entangled modulation, which requires a matrix description instead of scalar phase factors. Our work provides a direct instance of a machine detecting new phases and paves the way towards the development of automated tools to explore unsolved problems in many-body physics.
Anyonic excitations emerging from a Kitaev spin liquid can form a basis for quantum computers. Searching for such excitations motivated intense research on the honeycomb iridate materials. However, access to a spin liquid ground state has been hinder
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-$Gamma$ ($J$-$K$-$
The Kitaev spin liquid provides a rare example of well-established quantum spin liquids in more than one dimension. It is obtained as the exact ground state of the Kitaev spin model with bond-dependent anisotropic interactions. The peculiar interacti
Phase diagrams are an invaluable tool for material synthesis and provide information on the phases of the material at any given thermodynamic condition. Conventional phase diagram generation involves experimentation to provide an initial estimate of
We study the excitation spectrum of the spin-1 Kitaev model using the symmetric tensor network. By evaluating the virtual order parameters defined on the virtual Hilbert space in the tensor network formalism, we confirm the ground state is in a $math