Unsupervised machine learning of topological phase transitions*

In the traditional theory of phase transitions, pioneered by Landau, different phases are characterized by the symmetries they break. However, physical systems can also exhibit phase transitions between two states that share the same symmetries, but can be sharply distinguished by their “topological” properties. While symmetry-breaking phase transitions are readily captured with machine learning, topological phase transitions are significantly more difficult, which is related to their non-local nature. In this talk, I will discuss an unsupervised machine-learning approach that we propose [see Nature Physics 15, 790-795 (2019)], which is capable of “learning” topological invariants from raw, unlabeled data. The success of the approach is demonstrated on several different models and we also discuss a mapping of the output of the machine learning to the eigenvalues and wavefunctions of an auxiliary quantum problem. This will allow us to use physical intuition of quantum mechanics to understand how the machine-learning algorithm performs the topological classification.