Neural-Network Quantum Embedding Solvers for Correlated Materials

TL;DR

This paper introduces neural network-based impurity solvers that rapidly and accurately predict Green's functions in correlated materials, significantly speeding up quantum embedding calculations like DMFT.

Contribution

The authors develop neural network solvers trained on synthetic data that outperform traditional methods in speed while maintaining high accuracy for real materials and models.

Findings

Achieves orders-of-magnitude speedup over quantum Monte Carlo methods.

Successfully reproduces phase diagrams and electronic properties of complex materials.

Provides accurate impurity solutions for both model systems and real materials.

Abstract

Quantum impurity solvers are the computational bottleneck of quantum embedding approaches to correlated materials, such as dynamical mean-field theory (DMFT). We show that neural networks trained on synthetic, material-agnostic data learn the impurity mapping from hybridization functions and local interactions to Green's functions with quantitative accuracy for both model systems and real materials, providing fast solvers for single- and multi-orbital models. Benchmarks against numerically controlled quantum Monte Carlo show that the method reproduces the Mott transition, multi-orbital phase diagrams of Hubbard-Kanamori models, and the electronic properties of SrVO$_3$ and SrMnO$_3$. The learned solvers achieve orders-of-magnitude speedup and can initialize controlled calculations, dramatically accelerating DMFT while preserving accuracy.