Unsupervised and supervised learning of interacting topological phases from single-particle correlation functions

TL;DR

This paper demonstrates that machine learning techniques trained on data from non-interacting systems can accurately predict topological phases in interacting quantum models, bridging the gap between solvable and complex systems.

Contribution

It shows that unsupervised and supervised learning methods can identify topological phases in interacting systems using data from non-interacting models.

Findings

PCA and CNN trained on non-interacting data accurately identify topological phases.

Machine learning methods successfully reconstruct phase diagrams of interacting superconductors.

Unsupervised and supervised techniques can detect interaction-induced phases from non-interacting data.

Abstract

The recent advances in machine learning algorithms have boosted the application of these techniques to the field of condensed matter physics, in order e.g. to classify the phases of matter at equilibrium or to predict the real-time dynamics of a large class of physical models. Typically in these works, a machine learning algorithm is trained and tested on data coming from the same physical model. Here we demonstrate that unsupervised and supervised machine learning techniques are able to predict phases of a non-exactly solvable model when trained on data of a solvable model. In particular, we employ a training set made by single-particle correlation functions of a non-interacting quantum wire and by using principal component analysis, k-means clustering, and convolutional neural networks we reconstruct the phase diagram of an interacting superconductor. We show that both the principal component analysis and the convolutional neural networks trained on the data of the non-interacting model can identify the topological phases of the interacting model with a high degree of accuracy. Our findings indicate that non-trivial phases of matter emerging from the presence of interactions can be identified by means of unsupervised and supervised techniques applied to data of non-interacting systems.