Vision Transformer Neural Quantum States for Impurity Models

TL;DR

This paper introduces a Vision Transformer-based neural quantum state approach for impurity models, achieving high accuracy with fewer parameters and enabling efficient computation of dynamical properties like X-ray spectra.

Contribution

It adapts Vision Transformer architecture for quantum impurity models and demonstrates improved accuracy and efficiency over traditional methods.

Findings

ViT-based neural quantum states match or outperform matrix product states in accuracy.

The approach requires significantly fewer variational parameters.

It successfully computes dynamical quantities such as X-ray absorption spectra.

Abstract

Transformer neural networks, known for their ability to recognize complex patterns in high-dimensional data, offer a promising framework for capturing many-body correlations in quantum systems. We employ an adapted Vision Transformer (ViT) architecture to model quantum impurity models, optimizing it with a subspace expansion scheme that surpasses conventional variational Monte Carlo in both accuracy and efficiency. Benchmarks against matrix product states in single- and three-orbital Anderson impurity models show that these ViT-based neural quantum states achieve comparable or superior accuracy with significantly fewer variational parameters. We further extend our approach to compute dynamical quantities by constructing a restricted excitation space that effectively captures relevant physical processes, yielding accurate core-level X-ray absorption spectra. These findings highlight the potential of ViT-based neural quantum states for accurate and efficient modeling of quantum impurity models.