Inferring hidden symmetries of exotic magnets from detecting explicit order parameters.

Area of Science:

• Condensed Matter Physics
• Materials Science
• Machine Learning Applications

Background:

• Unconventional magnets can be understood by mapping them to simpler ferromagnets via high-symmetry points.
• Existing knowledge of ferromagnetic systems can offer insights into complex magnetic orders.

Purpose of the Study:

• To develop an unsupervised and interpretable machine learning (ML) method for discovering high-symmetry points in unconventional magnets.
• To apply this ML approach to the Heisenberg-Kitaev model on a honeycomb lattice without prior knowledge of symmetry points.

Main Methods:

• Utilizing an unsupervised machine learning algorithm to search for high-symmetry points.
• Applying the ML method to the Heisenberg-Kitaev model to learn symmetry transformations.
• Analyzing ordering matrices (D2 and D2h) for magnetization description.

Main Results:

• The ML method successfully identified hidden O(3) symmetry in the Heisenberg-Kitaev model without explicit training data.
• A set of D2 and D2h ordering matrices were found to provide a more comprehensive description of magnetization than stripy or zigzag orders.
• The ML model learned local constraints at phase boundaries, revealing subdimensional symmetry.

Conclusions:

• Explicit order parameters are crucial for understanding many-body spin systems.
• The interpretability of ML techniques is vital for their application in physical sciences.
• This work demonstrates a novel ML-driven approach to uncover fundamental symmetries in complex magnetic materials.