Machine learning for many-body physics: efficient solution of dynamical mean-field theory

TL;DR

This paper develops machine learning methods to efficiently solve dynamical mean-field theory equations, accurately predicting metallic and insulating states in the Hubbard model, potentially aiding real materials analysis.

Contribution

It introduces a machine learning approach for solving dynamical mean-field theory equations, focusing on mapping input to output functions and distinguishing phases.

Findings

Successfully predicts metallic and Mott insulator solutions.

Accurately reproduces correlation functions, quasi-particle weight, and particle density.

Shows potential for efficient real materials predictions.

Abstract

Machine learning methods for solving the equations of dynamical mean-field theory are developed. The method is demonstrated on the three dimensional Hubbard model. The key technical issues are defining a mapping of an input function to an output function, and distinguishing metallic from insulating solutions. Both metallic and Mott insulator solutions can be predicted. The validity of the machine learning scheme is assessed by comparing predictions of full correlation functions, of quasi-particle weight and particle density to values directly computed. The results indicate that with modest further development, machine learning approach may be an attractive computational efficient option for real materials predictions for strongly correlated systems.