Neural-Network Quantum Embedding Solvers for Correlated 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.