Detection of Phase Transitions in Quantum Spin Chains via Unsupervised Machine Learning

In the field of machine learning, there has been an important breakthrough in recent years. What was at the center of it is the deep learning by artificial neural networks mimicking human brains. By deepening a process part which repeats extracting feature quantities through nonlinear transformations, so-called hidden layer, data/class separability and the discriminability have dramatically improved. Recently, the machine learning techniques have found a wide variety of applications in condensed matter and statistical physics. Examples include detection of phase transition and acceleration of Monte Carlo simulation. Meanwhile, most of these studies are based on supervised learning under well-known results, and there are only a few previous examples applying unsupervised learning. In this research, we investigate quantum phase transitions in various quantum spin chains by using an autoencoder which is one of unsupervised learning methods. In particular, we will show that the autoencoder whose input is only short-range correlators is capable of detecting even topological phase transition from the large-D phase to the Haldane phase without using either topological invariants or entanglement spectra.