Language-inspired machine learning approach for solving strongly correlated problems with dynamical mean-field theory

Abstract

We present SCALINN—strongly correlated approach with language-inspired neural network—as a method for solving the Anderson impurity model and reducing the computational cost of dynamical mean-field theory calculations. Inspired by the success of generative Transformer networks in natural language processing, SCALINN utilizes an in-house modified Transformer network in order to learn correlated Matsubara Green's functions, which act as solutions to the impurity model. This is achieved by providing the network with low-cost Matsubara Green's functions, thereby overcoming the computational cost of high accuracy solutions. Across different temperatures and interaction strengths, the performance of SCALINN is demonstrated in both physical observables (spectral function, Matsubara Green's functions, quasiparticle weight), and the mean squared error cost values of the neural network, showcasing the network's ability to accelerate Green's function based calculations of correlated materials by predicting DMFT solver solutions, which—given a sufficiently comprehensive training database—can be applied across materials and regimes, enabling DFT + DMFT calculations without prior knowledge of the material properties.