Principal component analysis on identifying topological quantum states

Min-Ruei Lin^1*, Wan-Ju Li¹, Shin-Ming Huang¹

¹Department of Physics, National Sun Yat-sen University, Kaohsiung 804, Taiwan

* Presenter:Min-Ruei Lin, email:m082030021@student.nsysu.edu.tw

Powerful machine learning techniques are widely studied and applied in scientific fields in recent years. Among many techniques, Principal component analysis (PCA) as a method of unsupervised learning has achieved a great success in distilling information and identifying patterns in data. The basic idea of PCA is to project data into the reduced space spanned by major eigenmodes of the data’s covariance, which may be powerful in classifying topological states. In this work, we utilize PCA to examine the convolution of quantum states for classifying 1D and 2D topological systems, whose topological invariants are the winding number and the Chern number respectively. Different from classical systems, the quantum systems need judicious gauge fixing, especially in 2D topological systems where a globally continuous wave function is impossible. Our results demonstrate that eigenmodes can be good representations of topological orders.

Keywords: machine learning, PCA, topology, winding number, Chern number