Topological quantum phase transitions retrieved through unsupervised machine learning

Detecting topological features in physics with unsupervised machine learning has been attracting increasing attention recently. It provides a viable learning framework for the study of topological phase transitions, without prior knowledge and labeled training examples of the system.
Here we show with several prototypical and relevant models that topological quantum phase transitions can indeed be automatically retrieved, with unsupervised machine learning, and requiring only a very limited number of hyperparameters. Inspired by the non-Euclidean structure of the data set as well as the concept of manifold learning, we argue that the widely used choice of a Euclidean distance may in general be suboptimal to discover topological transitions in momentum space. On the other hand, we can show that the Chebyshev distance sharpens the characteristic features of topological transitions, and thus decisively supports the retrieval of the critical points. Implications and demonstrations for learning in real space will also be provided.

Reference: Y. Che, C. Gneiting, T. Liu, F. Nori, arXiv:2002.02363 (to appear in Physical Review B).