Abstract: I present the Tensorial Kernel Support Vector Machine (TK-SVM) as a tool to automate the classification of complicated phase diagrams for classical systems, which is a complicated task when multiple phases coexist and orders compete, as is frequently the case in frustrated magnetism. The key property is the interpretability of the decision function, from which the physical local order parameter can be deduced irrespective of its rank. Furthermore, we discuss a second intrinsic parameter of TK-SVM, the bias, which can be given a distinct physical meaning and which allows one to make an unsupervised graph analysis of the topology of the phase diagram. We illustrate our tool for the classical XXZ model on the frustrated pyrochlore lattice. Unexpectedly, TK-SVM could also learn local constraints hinting at various types of spin liquids resulting in a complete classification of all types of behavior for this model. TK-SVM was subsequently applied to the Kitaev materials where we found a new type of magnetic order as well as new explicit formula’s for the local constraints of certain spin liquids, proving the usefulness of TK-SVM in going beyond the state of the art.
Phys. Rev. B 99, 060404 (2019)
Phys. Rev. B 99, 104410 (2019)
Phys. Rev. B 100, 174408 (2019)
preprint arXiv:2004.14415 (2020)