Data-Driven Dynamical Mean-Field Theory: an error-correction approach to solve the quantum many-body problem using machine learning

TL;DR

This paper introduces d3MFT, a machine learning-based error correction method that accelerates and improves the accuracy of solving the Anderson Impurity Model within dynamical mean-field theory, enabling efficient study of strongly correlated materials.

Contribution

It presents a novel ensemble error-correction approach using machine learning to solve the Anderson Impurity Model more efficiently within DMFT.

Findings

Achieves faster AIM solutions with high accuracy

Validates approach with Mott transition in Hubbard model

Demonstrates potential for studying complex correlated systems

Abstract

Machine learning opens new avenues for modelling correlated materials. Quantum embedding approaches, such as the dynamical mean-field theory (DMFT), provide corrections to first-principles calculations for strongly correlated materials, which are poorly described at lower levels of theory. Such embedding approaches are computationally demanding on classical computing architectures, and hence remain restricted to small systems, which limits the scope of applicability without exceptional computational resources. Here we outline a data-driven machine learning process for solving the Anderson Impurity Model (AIM) - the central component of DMFT calculations. The key advance is the use of an ensemble error-correction approach to generate fast and accurate solutions of AIM. An example calculation of the Mott transition using DMFT in the single band Hubbard model is given as an example of the technique, and is validated against the most accurate available method. This new approach is called data-driven dynamical mean-field theory (\textbf{d$^{3}$MFT}).