ABSTRACT
This chapter describes the usage of ML to study condensed matter. ML is shown to accelerate the sampling of spin glass configurations in computer simulations by up to five orders of magnitude. On the analysis side, ML is very efficient for evaluating the output of simulations of topological order transitions. The latter are characterized by the temperature-driven unbinding of vortex/antivortex pairs. Such transitions may be detected by analyzing configurations using neural networks implemented with the aim of learning vortices. Incorporated in the heart of computer simulations, ML is used to study quantum many-body systems. Here, the mathematical object describing the quantum-mechanical state of a system – the many-body wave function – is implemented in a neural-network representation. Away from pure theory, ML allows the quantum state of a system to be reconstructed based on experimental measurements. Here, the experimental data are used to train a neural network via unsupervised learning to output the state as a neural-network quantum state. As a more technological application, ML is efficient in predicting new materials with desired properties. Neural networks or other ML techniques enable the prediction of thermodynamically stable compounds with a desired structure by searching over the entire compound space.
