Deep machine learning the spectral function of a hole in a quantum antiferromagnet

Understanding charge motion in a background of interacting quantum spins is a basic problem in quantum many-body physics. The most extensively studied model for this problem is the so-called t-t'-t''-J model, where the determination of the parameter t' in the context of cuprate superconductors was inconclusive. Here we present a theoretical study of the spectral functions of a mobile hole in the t-t'-t''-J model using a classical machine learning (ML) method, namely K-nearest neighbors (KNN), and a deep ML method, namely fully connected feed-forward neural network (FFNN). We employ the self-consistent Born approximation to generate the training, validation, and testing dataset consisting of about 1.3x10^5 spectral functions and introduce an algorithm that reduces the ML dimensionality by 25%. We show that for the forward problem, both ML methods allow for accurate spectral functions to be calculated in significantly less time than the physical theory that produces the data, allowing for rapid search through parameter space. Furthermore, we find that for the inverse problem, FFNN can, but KNN cannot, accurately predict the model parameters using merely the density-of-state spectrum. Our results suggest that it may be possible to use deep learning methods to predict material parameters from experimentally measured spectral functions.