Machine Learning Green's Functions of Strongly Correlated Hubbard Models

TL;DR

This paper introduces a machine learning approach using kernel ridge regression to predict self-energy and spectral functions of one-dimensional Hubbard models across various interaction strengths, leveraging mean-field features.

Contribution

It presents a novel ML framework that accurately predicts Green's functions of Hubbard models using only mean-field and first-order GW features, applicable to complex interactions.

Findings

Accurately predicts self-energy across a wide range of U/t values.

Transforms predicted self-energy to real-frequency Green's function and spectral properties.

Applicable to models with long-range hopping terms.

Abstract

We demonstrate that a machine learning framework based on kernel ridge regression can encode and predict the self-energy of one-dimensional Hubbard models using only mean-field features such as static and dynamic Hartree-Fock quantities and first-order GW calculations. This approach is applicable across a wide range of on-site Coulomb interaction strengths $U/t$, ranging from weakly interacting systems ($U/t \ll 1$) to strong correlations ($U/t > 8$). The predicted self-energy is transformed via Dyson's equation and analytic continuation to obtain the real-frequency Green's function, which allows access to the spectral function and density of states. This method can be used for nearest-neighbor interactions $t$ and long-range hopping terms $t'$, $t''$, and $t'''$.