Physics-informed neural network model for quantum impurity problems based on Lehmann representation

TL;DR

This paper introduces a physics-informed neural network that accurately predicts the self-energy in quantum impurity models using Lehmann representation, significantly improving prediction accuracy across various parameters.

Contribution

The paper presents a novel PINN approach leveraging Lehmann representation to efficiently model self-energy in Anderson impurity models, enhancing accuracy and physical consistency.

Findings

High accuracy in predicting self-energy across parameter ranges

Lehmann representation reduces test error by approximately 7.8 times

Effective incorporation of physical constraints improves model performance

Abstract

We propose a physics-informed neural network (PINN) model to efficiently predict the self-energy of Anderson impurity models (AIMs) based on the Lehmann representation. As an example, we apply the PINN model to a single-orbital AIM (SAIM) for a noninteracting electron bath with a semicircular density of states. Trained across a wide range of onsite Coulomb interactions $U$ and hybridization strengths $V$, the PINN model demonstrates high accuracy in both $U$-$V$ and Matsubara-frequency spaces. Additionally, we investigate the effectiveness of physical constraints implemented in the PINN model. For example, We show that the Lehmann representation allows the PINN model to reduce the maximum test error in an electron filling by a factor of approximately 7.8.