Revealing the Phase Diagram of Kitaev Materials by Machine Learning: Cooperation and Competition between Spin Liquids
This work addresses the challenge of understanding complex quantum phases in materials science, offering an automated tool for many-body physics, though it is incremental in applying existing ML methods to a new domain.
The researchers tackled the problem of mapping the phase diagram of Kitaev materials using an unsupervised machine learning method, revealing multiple spin liquids and exotic magnetic orders, and found that key physics can be understood classically.
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-$Γ$ 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 $Γ$ 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.