Probing hidden spin order with interpretable machine learning

Abstract

The search of unconventional magnetic and nonmagnetic states is a major topic in the study of frustrated magnetism. Canonical examples of those states include various spin liquids and spin nematics. However, discerning their existence and the correct characterization is usually challenging. Here we introduce a machine-learning protocol that can identify general nematic order and their order parameter from seemingly featureless spin configurations, thus providing comprehensive insight on the presence or absence of hidden orders. We demonstrate the capabilities of our method by extracting the analytical form of nematic order parameter tensors up to rank 6. This may prove useful in the search for novel spin states and for ruling out spurious spin liquid candidates.

The source codes for reproducing our results are available under an open-source license on our department’s GitLab server.

Refer to the README for detailed instructions on building and running our codes. Feel free to reach out in case of problems.

Supplemental Materials

We elaborate some of the more technical details of our work in the Supplemental Materials at the end of the ArXiv preprint, in particular:

• the redundancy in the monomial mapping and how we account for it;
• the regularization parameter in SVM and its reformulation, $$\nu$$-SVM in terms of a more controlled regularization parameter $$\nu$$ and the influence of its choice in the physical problem;
• the decoding of the block structure of the coefficient matrix for the rank-6 symmetry $$I_h$$.

We also provide raw data from our simulations of the symmetries covered in the paper:

• $$T_d$$: full coefficient matrix (TXT + PNG), block structure (TXT + PNG);
• $$O_h$$, $$T_h$$: full coefficient matrix (PNG), block structure (TXT + PNG);
• $$I_h$$: block structure (TXT + PNG), decoded coefficients of order parameter tensor.