Neural network impurity solver for real-frequency dynamical mean-field theory

TL;DR

This paper presents a neural network-based impurity solver for real-frequency dynamical mean-field theory, utilizing a multihead cross-attention mechanism trained on high-quality data to accurately predict spectral functions across different electronic regimes.

Contribution

The authors develop a novel neural network impurity solver with a multihead cross-attention architecture that generalizes smoothly to real frequencies, improving accuracy in DMFT calculations.

Findings

Achieves quantitative accuracy in Hubbard model simulations

Successfully models metallic, correlated, and insulating regimes

Demonstrates smooth generalization to real-frequency axis

Abstract

We introduce a neural network impurity solver for real-frequency DMFT that employs a multihead cross-attention mechanism to map hybridization functions to spectral functions, conditioned on impurity parameters. Trained on high-quality MPS data from complex contour time evolution and incorporating derivative constraints with respect to the complex-time angle, our model achieves smooth generalization to the real-frequency axis. Benchmarking on the single-band Hubbard model for the Bethe lattice demonstrates quantitative accuracy across metallic, strongly correlated, and insulating regimes.