Predicting interacting Green's functions with neural networks

TL;DR

This paper introduces a machine learning framework that predicts interacting Green's functions in strongly correlated materials, significantly reducing computational costs of DMFT calculations while maintaining accuracy.

Contribution

The authors develop a two-step neural network approach that accelerates DMFT simulations by predicting Green's functions directly from band structures, offering a scalable alternative to traditional methods.

Findings

The ML model accurately predicts Green's functions across various lattice structures.

The approach reduces computational time compared to conventional quantum impurity solvers.

The method maintains physical plausibility and can be extended to multi-band systems.

Abstract

Strongly correlated materials exhibit complex electronic phenomena that are challenging to capture with traditional theoretical methods, yet understanding these systems is crucial for discovering new quantum materials. Addressing the computational bottlenecks in studying such systems, we present a proof-of-concept machine learning-based approach to accelerate Dynamical Mean Field Theory (DMFT) calculations. Our method predicts interacting Green's functions on arbitrary two-dimensional lattices using a two-step ML framework. First, an autoencoder-based network learns and generates physically plausible band structures of materials, providing diverse training data. Next, a dense neural network predicts interacting Green's functions of these physically-possible band structures, expressed in the basis of Legendre polynomials. We demonstrate that this architecture can serve as a substitute for the computationally demanding quantum impurity solver in DMFT, significantly reducing computational cost while maintaining accuracy. This approach offers a scalable pathway to accelerate simulations of strongly correlated systems and lays the groundwork for future extensions to multi-band systems.