Quantum phase recognition via unsupervised machine learning

TL;DR

This paper introduces an unsupervised machine learning method using convolutional neural networks combined with quantum Monte Carlo sampling to identify and map phase diagrams of many-body quantum systems without prior knowledge.

Contribution

It presents a generalized, unsupervised approach that accurately detects various phase transitions and complex phases in interacting quantum systems.

Findings

Successfully mapped phase diagrams of boson and fermion models.

Identified first-order, second-order, and Kosterlitz-Thouless transitions.

Detected non-trivial phases like superfluids and topologically ordered states.

Abstract

The application of state-of-the-art machine learning techniques to statistical physic problems has seen a surge of interest for their ability to discriminate phases of matter by extracting essential features in the many-body wavefunction or the ensemble of correlators sampled in Monte Carlo simulations. Here we introduce a gener- alization of supervised machine learning approaches that allows to accurately map out phase diagrams of inter- acting many-body systems without any prior knowledge, e.g. of their general topology or the number of distinct phases. To substantiate the versatility of this approach, which combines convolutional neural networks with quantum Monte Carlo sampling, we map out the phase diagrams of interacting boson and fermion models both at zero and finite temperatures and show that first-order, second-order, and Kosterlitz-Thouless phase transitions can all be identified. We explicitly demonstrate that our approach is capable of identifying the phase transition to non-trivial many-body phases such as superfluids or topologically ordered phases without supervision.