Neural Network Study for 1+1d-Complex Scalar Field Theory

Abstract

Modern Deep Learning techniques are employed in the context of two dimensional lattice complex scalar field theory, which has a non-trivial phase diagram at nonzero temperature and chemical potential. We demonstrated that deep neural networks can identify the phase transition in a semi-supervised manner, and can also discover hidden correlations beyond conventional analysis in decoding phase transition information with restricted input. We further showed that the network can efficiently learn the physical observables with limited training samples, which thus render an effective non-linear regression method in capturing the physical observables. Finally we explored generating new configurations with generative adversarial network (GAN), where we found the GAN can automatically capture the implicit local constraint for the physical configurations and also the underlying physical distribution.